the 1 isometry classes of irreducible [16,12,4]_4 codes are:

code no       1:
================
1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0
2 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0
1 2 1 0 0 0 1 0 0 0 0 0 0 0 0 0
2 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0
1 2 0 1 0 0 0 0 1 0 0 0 0 0 0 0
3 2 1 1 0 0 0 0 0 1 0 0 0 0 0 0
2 3 1 1 0 0 0 0 0 0 1 0 0 0 0 0
1 0 2 1 0 0 0 0 0 0 0 1 0 0 0 0
0 1 2 1 0 0 0 0 0 0 0 0 1 0 0 0
3 3 2 1 0 0 0 0 0 0 0 0 0 1 0 0
3 0 3 1 0 0 0 0 0 0 0 0 0 0 1 0
2 2 3 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:
(
1 0 0 0 
0 1 0 0 
3 3 3 3 
2 2 1 3 
, 0
, 
2 0 0 0 
0 3 0 0 
2 1 0 2 
1 2 3 3 
, 1
, 
3 0 0 0 
3 0 3 2 
0 3 2 3 
2 0 1 2 
, 1
, 
3 0 0 0 
3 2 3 0 
3 3 2 1 
0 0 0 1 
, 1
, 
0 3 0 0 
3 0 0 0 
3 3 1 2 
0 0 1 0 
, 1
, 
3 3 3 3 
2 1 0 2 
0 0 3 0 
1 0 1 3 
, 1
, 
3 3 2 1 
0 0 1 0 
2 0 0 0 
1 1 2 3 
, 1
)
acting on the columns of the generator matrix as follows (in order):
(3, 5)(4, 14)(6, 11)(7, 10)(8, 13)(9, 12), 
(3, 12, 5, 9)(4, 7, 14, 10)(6, 13, 11, 8)(15, 16), 
(2, 15)(3, 8, 5, 13)(4, 9, 14, 12)(6, 7, 11, 10), 
(2, 11, 12, 7)(3, 10, 9, 16)(5, 6)(8, 13, 15, 14), 
(1, 2)(3, 4, 5, 14)(6, 8, 11, 13)(7, 9, 10, 12), 
(1, 8, 13, 5)(2, 7, 14, 9)(4, 10, 11, 15)(6, 12), 
(1, 3, 2, 14, 4, 8, 12, 16)(5, 9, 7, 10, 6, 15, 11, 13)
orbits: { 1, 2, 5, 16, 15, 7, 9, 3, 12, 8, 6, 4, 13, 11, 10, 14 }