the 9 isometry classes of irreducible [15,12,4]_16 codes are:

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

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

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

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

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

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

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

code no       8:
================
1 1 1 1 0 0 0 0 0 0 0 0 0 0 0
3 2 1 0 1 0 0 0 0 0 0 0 0 0 0
5 3 1 0 0 1 0 0 0 0 0 0 0 0 0
2 4 1 0 0 0 1 0 0 0 0 0 0 0 0
12 5 1 0 0 0 0 1 0 0 0 0 0 0 0
14 6 1 0 0 0 0 0 1 0 0 0 0 0 0
10 7 1 0 0 0 0 0 0 1 0 0 0 0 0
11 8 1 0 0 0 0 0 0 0 1 0 0 0 0
13 9 1 0 0 0 0 0 0 0 0 1 0 0 0
9 10 1 0 0 0 0 0 0 0 0 0 1 0 0
6 11 1 0 0 0 0 0 0 0 0 0 0 1 0
8 12 1 0 0 0 0 0 0 0 0 0 0 0 1
the automorphism group has order 24
and is strongly generated by the following 4 elements:
(
14 0 0 
15 1 11 
1 1 1 
, 2
, 
0 0 15 
0 15 0 
15 0 0 
, 2
, 
15 7 11 
12 4 11 
12 7 8 
, 0
, 
1 10 13 
6 6 6 
11 2 15 
, 1
)
acting on the columns of the generator matrix as follows (in order):
(2, 13)(3, 4)(6, 9)(7, 15)(10, 11), 
(1, 3)(7, 12)(8, 13)(9, 14)(10, 11), 
(1, 7)(2, 6)(3, 12)(4, 15)(8, 9)(10, 11)(13, 14), 
(1, 13, 12, 9)(2, 15, 6, 4)(3, 8, 7, 14)
orbits: { 1, 3, 7, 9, 4, 12, 14, 15, 8, 6, 13, 2 }, { 5 }, { 10, 11 }

code no       9:
================
1 1 1 1 0 0 0 0 0 0 0 0 0 0 0
3 2 1 0 1 0 0 0 0 0 0 0 0 0 0
12 3 1 0 0 1 0 0 0 0 0 0 0 0 0
8 5 1 0 0 0 1 0 0 0 0 0 0 0 0
15 6 1 0 0 0 0 1 0 0 0 0 0 0 0
9 7 1 0 0 0 0 0 1 0 0 0 0 0 0
6 8 1 0 0 0 0 0 0 1 0 0 0 0 0
4 9 1 0 0 0 0 0 0 0 1 0 0 0 0
13 10 1 0 0 0 0 0 0 0 0 1 0 0 0
14 11 1 0 0 0 0 0 0 0 0 0 1 0 0
11 12 1 0 0 0 0 0 0 0 0 0 0 1 0
2 13 1 0 0 0 0 0 0 0 0 0 0 0 1
the automorphism group has order 120
and is strongly generated by the following 6 elements:
(
14 0 0 
0 15 0 
12 9 15 
, 1
, 
4 0 0 
13 11 12 
0 0 14 
, 2
, 
0 0 6 
13 8 1 
14 0 0 
, 2
, 
3 14 5 
6 10 8 
5 2 13 
, 1
, 
10 11 5 
14 13 9 
13 8 11 
, 0
, 
9 9 9 
12 15 2 
3 5 4 
, 1
)
acting on the columns of the generator matrix as follows (in order):
(3, 8, 12, 15)(4, 9, 13, 14)(5, 10, 6, 11), 
(2, 7)(4, 5)(6, 13)(9, 10)(11, 14), 
(1, 3)(2, 6)(4, 14)(5, 11)(7, 13)(8, 12), 
(1, 12, 3, 8)(2, 4, 6, 14)(5, 13, 11, 7)(9, 10), 
(1, 15)(2, 9)(3, 8)(4, 5)(6, 14)(7, 10)(11, 13), 
(1, 11, 13, 12, 2, 14, 3, 5, 7, 8, 6, 4)(9, 15, 10)
orbits: { 1, 3, 8, 15, 4, 12, 14, 7, 9, 5, 2, 6, 13, 11, 10 }