the 4 isometry classes of irreducible [12,8,5]_16 codes are:

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

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

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

code no       4:
================
1 1 1 1 1 0 0 0 0 0 0 0
4 3 2 1 0 1 0 0 0 0 0 0
3 8 5 1 0 0 1 0 0 0 0 0
11 15 6 1 0 0 0 1 0 0 0 0
10 4 9 1 0 0 0 0 1 0 0 0
7 13 10 1 0 0 0 0 0 1 0 0
8 14 11 1 0 0 0 0 0 0 1 0
5 11 12 1 0 0 0 0 0 0 0 1
the automorphism group has order 240
and is strongly generated by the following 6 elements:
(
7 0 0 0 
0 2 0 0 
0 0 10 0 
0 0 0 9 
, 2
, 
10 0 0 0 
13 5 4 2 
0 0 9 0 
13 15 7 8 
, 2
, 
12 0 0 0 
0 0 0 6 
0 0 15 0 
0 9 0 0 
, 1
, 
0 0 0 9 
0 0 9 0 
0 9 0 0 
9 0 0 0 
, 2
, 
12 5 8 14 
0 0 0 12 
1 3 5 15 
0 11 0 0 
, 3
, 
4 1 3 11 
11 0 0 0 
3 3 3 3 
0 0 14 0 
, 1
)
acting on the columns of the generator matrix as follows (in order):
(5, 7)(6, 8)(9, 10)(11, 12), 
(2, 9)(4, 6)(7, 10)(8, 11), 
(2, 4)(5, 8, 7, 6)(9, 12, 10, 11), 
(1, 4)(2, 3)(6, 10)(8, 9), 
(1, 9, 10, 11)(2, 4)(3, 6, 8, 7), 
(1, 2, 8, 12)(3, 4, 10, 5)(6, 9)
orbits: { 1, 4, 11, 12, 6, 2, 3, 8, 10, 9, 7, 5 }