Code 16k is interesting because it's essentially a lot of reverse-video code128 rows stacked on top of one another, with some bearer bars, start/stop characters, a start symbol, padding, and check symbols thrown in.

Code 16k has 6 modes:

Mode	Starting Code Set	Starting Shift Mode
0	A	none
1	B	none
2	C	none
3	B	FNC1
4	C	FNC1
5	C	1SB
6	C	2SB

FNC1, or "function 1" means that the data following is to be interpreted as a UPC would be. 1SB and 2SB are "single-shift B" and "double shift B" meaning that the next or next 2 characters are from character set B, respectively. FNCs and Shifts are also defined in the character set.

A Code 16k block may contain up to 16 rows, separated by horizontal bearer bars. The top and bottom of the symbol have longer bearer bars to include a leading and trailing quiet zone. Each row has its own start and stop character and contains 5 symbols. PAD characters must be inserted to make a row contain 5 symbols if necessary. Here are the start and stop patterns:

ROW	START	STOP
1	3 -2 1 -1 1	-3 2 -1 1
2	2 -2 2 -1 1	-2 2 -2 1
3	2 -1 2 -2 1	-2 1 -2 2
4	1 -4 1 -1 1	-1 4 -1 1
5	1 -1 3 -2 1	-1 1 -3 2
6	1 -2 3 -1 1	-1 2 -3 1
7	1 -1 1 -4 1	-1 1 -1 4
8	3 -1 1 -2 1	-3 1 -1 2
9	3 -2 1 -1 1	-1 1 -3 2
10	2 -2 2 -1 1	-1 2 -3 1
11	2 -1 2 -2 1	-1 1 -1 4
12	1 -4 1 -1 1	-3 1 -1 2
13	1 -1 3 -2 1	-3 2 -1 1
14	1 -2 3 -1 1	-2 2 -2 1
15	1 -1 1 -4 1	-2 1 -2 2
16	3 -1 1 -2 1	-1 4 -1 1

Symbols may be concatenated by making FNC2 the first character following the starting symbol. Each subsequent pattern is appended to the preceding pattern. It is also possible to concatenate in a random order by making the value of the first symbol following the start symbol equal to 10 times the symbol number plus the total number of symbols (not to exceed 9). For example, the 4th block out of 8 would encode to 48. In this case, the next symbol should be FNC2 (ie, [ 48, FNC2 ]).

The start symbol is calculated to be 7 times the number of rows-2, plus the mode. [ 7(r-2)+m ]. Modes are defined in the table above.

Here is the table of characters and their patterns:

A	B	C	VALUE	BAR/Space Values
		00	0	-2 1 -2 2 -2 2
!	!	01	1	-2 2 -2 1 -2 2
"	"	02	2	-2 2 -2 2 -2 1
#	#	03	3	-1 2 -1 2 -2 3
$	$	04	4	-1 2 -1 3 -2 2
%	%	05	5	-1 3 -1 2 -2 2
&	&	06	6	-1 2 -2 2 -1 3
'	'	07	7	-1 2 -2 3 -1 2
(	(	08	8	-1 3 -2 2 -1 2
)	)	09	9	-2 2 -1 2 -1 3
*	*	10	10	-2 2 -1 3 -1 2
+	+	11	11	-2 3 -1 2 -1 2
,	,	12	12	-1 1 -2 2 -3 2
-	-	13	13	-1 2 -2 1 -3 2
.	.	14	14	-1 2 -2 2 -3 1
/	/	15	15	-1 1 -3 2 -2 2
0	0	16	16	-1 2 -3 1 -2 2
1	1	17	17	-1 2 -3 2 -2 1
2	2	18	18	-2 2 -3 2 -1 1
3	3	19	19	-2 2 -1 1 -3 2
4	4	20	20	-2 2 -1 2 -3 1
5	5	21	21	-2 1 -3 2 -1 2
6	6	22	22	-2 2 -3 1 -1 2
7	7	23	23	-3 1 -2 1 -3 1
8	8	24	24	-3 1 -1 2 -2 2
9	9	25	25	-3 2 -1 1 -2 2
:	:	26	26	-3 2 -1 2 -2 1
;	;	27	27	-3 1 -2 2 -1 2
<	<	28	28	-3 2 -2 1 -1 2
=	=	29	29	-3 2 -2 2 -1 1
>	>	30	30	-2 1 -2 1 -2 3
?	?	31	31	-2 1 -2 3 -2 1
@	@	32	32	-2 3 -2 1 -2 1
A	A	33	33	-1 1 -1 3 -2 3
B	B	34	34	-1 3 -1 1 -2 3
C	C	35	35	-1 3 -1 3 -2 1
D	D	36	36	-1 1 -2 3 -1 3
E	E	37	37	-1 3 -2 1 -1 3
F	F	38	38	-1 3 -2 3 -1 1
G	G	39	39	-2 1 -1 3 -1 3
H	H	40	40	-2 3 -1 1 -1 3
I	I	41	41	-2 3 -1 3 -1 1
J	J	42	42	-1 1 -2 1 -3 3
K	K	43	43	-1 1 -2 3 -3 1
L	L	44	44	-1 3 -2 1 -3 1
M	M	45	45	-1 1 -3 1 -2 3
N	N	46	46	-1 1 -3 3 -2 1
O	O	47	47	-1 3 -3 1 -2 1
P	P	48	48	-3 1 -3 1 -2 1
Q	Q	49	49	-2 1 -1 3 -3 1
R	R	50	50	-2 3 -1 1 -3 1
S	S	51	51	-2 1 -3 1 -1 3
T	T	52	52	-2 1 -3 3 -1 1
U	U	53	53	-2 1 -3 1 -3 1
V	V	54	54	-3 1 -1 1 -2 3
W	W	55	55	-3 1 -1 3 -2 1
X	X	56	56	-3 3 -1 1 -2 1
Y	Y	57	57	-3 1 -2 1 -1 3
Z	Z	58	58	-3 1 -2 3 -1 1
[	[	59	59	-3 3 -2 1 -1 1
\	\	60	60	-3 1 -4 1 -1 1
]	]	61	61	-2 2 -1 4 -1 1
^	^	62	62	-4 3 -1 1 -1 1
_	_	63	63	-1 1 -1 2 -2 4
^@~NUL	`	64	64	-1 1 -1 4 -2 2
^A~SOH	a	65	65	-1 2 -1 1 -2 4
^B~STX	b	66	66	-1 2 -1 4 -2 1
^C~ETX	c	67	67	-1 4 -1 1 -2 2
^D~EOT	d	68	68	-1 4 -1 2 -2 1
^E~ENQ	e	69	69	-1 1 -2 2 -1 4
^F~ACK	f	70	70	-1 1 -2 4 -1 2
^G~BEL	g	71	71	-1 2 -2 1 -1 4
^H~BS	h	72	72	-1 2 -2 4 -1 1
^I~HT	i	73	73	-1 4 -2 1 -1 2
^J~LF	j	74	74	-1 4 -2 2 -1 1
^K~VT	k	75	75	-2 4 -1 2 -1 1
^L~FF	l	76	76	-2 2 -1 1 -1 4
^M~CR	m	77	77	-4 1 -3 1 -1 1
^N~SO	n	78	78	-2 4 -1 1 -1 2
^O~SI	o	79	79	-1 3 -4 1 -1 1
^P~DLE	p	80	80	-1 1 -1 2 -4 2
^Q~DC1	q	81	81	-1 2 -1 1 -4 2
^R~DC2	r	82	82	-1 2 -1 2 -4 1
^S~DC3	s	83	83	-1 1 -4 2 -1 2
^T~DC4	t	84	84	-1 2 -4 1 -1 2
^U~NAK	u	85	85	-1 2 -4 2 -1 1
^V~SYN	v	86	86	-4 1 -1 2 -1 2
^W~ETB	w	87	87	-4 2 -1 1 -1 2
^X~CAN	x	88	88	-4 2 -1 2 -1 1
^Y~EM	y	89	89	-2 1 -2 1 -4 1
^Z~SUB	z	90	90	-2 1 -4 1 -2 1
^[~ESC	{	91	91	-4 1 -2 1 -2 1
^\~FS	|	92	92	-1 1 -1 1 -4 3
^]~GS	}	93	93	-1 1 -1 3 -4 1
^^~RS	~	94	94	-1 3 -1 1 -4 1
^_~US	^?~DEL	95	95	-1 1 -4 1 -1 3
FNC3	FNC3	96	96	-1 1 -4 3 -1 1
FNC2	FNC2	97	97	-4 1 -1 1 -1 3
1SB	1SA	98	98	-4 1 -1 3 -1 1
CODEC	CODEC	99	99	-1 1 -3 1 -4 1
CODEB	FNC4	CODEB	100	-1 1 -4 1 -3 1
FNC4	CODEA	CODEA	101	-3 1 -1 1 -4 1
FNC1	FNC1	FNC1	102	-4 1 -1 1 -3 1
PAD	PAD	PAD	103	-2 1 -1 4 -1 2
2SB	2SA	1SA	104	-2 1 -1 2 -1 4
2SC	2SC	2SB	105	-2 1 -1 2 -3 2
3SC	3SC	3SB	106	-2 3 -3 3

To read either of the pattern tables here, consider positive numbers to be a bar width and negative numbers to be a space width.

There are 2 checksums at the end of the code, which are calculated by weighting the sum of the values of each character including the start character. The first check symbol starts the weighting at 2, and the second starts weighting at 1. Next, take the modulo 107 of the sum. So if you had the character values 22, 10, 15, 20, the two checksums would be:
(2*22 + 3*10 + 4*15 + 5*20) % 107
(1*22 + 2*10 + 3*15 + 4*20) % 107

You can make a code16k barcode here. Only mode 1 is supported.

Codabar	Code 2 of 5	Code 3 of 9	Interleaved 2 of 5
Postnet	UPC	Code 128	Code 16k