the 1 isometry classes of irreducible [16,12,5]_16 codes are:

code no       1:
================
1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0
4 3 2 1 0 1 0 0 0 0 0 0 0 0 0 0
3 8 5 1 0 0 1 0 0 0 0 0 0 0 0 0
11 15 6 1 0 0 0 1 0 0 0 0 0 0 0 0
15 9 7 1 0 0 0 0 1 0 0 0 0 0 0 0
12 6 8 1 0 0 0 0 0 1 0 0 0 0 0 0
10 4 9 1 0 0 0 0 0 0 1 0 0 0 0 0
7 13 10 1 0 0 0 0 0 0 0 1 0 0 0 0
8 14 11 1 0 0 0 0 0 0 0 0 1 0 0 0
5 11 12 1 0 0 0 0 0 0 0 0 0 1 0 0
9 2 13 1 0 0 0 0 0 0 0 0 0 0 1 0
6 7 14 1 0 0 0 0 0 0 0 0 0 0 0 1
the automorphism group has order 960
and is strongly generated by the following 7 elements:
(
5 0 0 0 
0 9 0 0 
9 13 15 3 
6 1 7 4 
, 1
, 
8 0 0 0 
8 7 11 6 
7 11 6 3 
0 0 0 3 
, 2
, 
15 0 0 0 
4 6 9 11 
7 11 1 5 
12 5 8 14 
, 3
, 
13 0 0 0 
0 0 0 6 
11 2 15 5 
6 2 13 3 
, 2
, 
10 1 8 6 
9 4 10 5 
3 13 4 15 
1 0 0 0 
, 2
, 
0 0 4 0 
11 9 6 4 
2 14 8 5 
9 7 10 6 
, 1
, 
10 2 11 8 
14 6 2 13 
12 8 2 5 
9 11 2 15 
, 2
)
acting on the columns of the generator matrix as follows (in order):
(3, 13, 14, 10)(4, 6, 7, 12)(5, 8, 16, 9)(11, 15), 
(2, 8)(3, 11)(5, 9)(6, 10)(7, 14)(12, 15), 
(2, 5, 8, 9)(3, 6, 11, 10)(4, 13)(7, 12, 14, 15), 
(2, 13, 11, 16, 15, 4)(3, 5, 12, 7, 8, 10)(6, 14, 9), 
(1, 4, 13)(2, 14, 3, 8, 7, 11)(5, 10, 12, 9, 6, 15), 
(1, 6, 10, 3)(2, 13, 12, 9)(4, 5, 15, 7)(8, 14), 
(1, 15, 7, 9, 5, 16)(2, 14, 8, 3, 6, 13)(4, 11, 12)
orbits: { 1, 13, 3, 16, 4, 2, 6, 10, 11, 14, 8, 5, 12, 15, 7, 9 }