the 3 isometry classes of irreducible [15,4,9]_3 codes are:

code no       1:
================
1 1 1 1 1 1 1 1 1 1 1 2 0 0 0
2 2 2 2 1 1 1 1 0 0 0 0 2 0 0
2 2 1 0 2 2 1 0 1 1 0 0 0 2 0
2 1 2 1 2 0 0 1 2 1 0 0 0 0 2
the automorphism group has order 78
and is strongly generated by the following 4 elements:
(
1 0 0 0 0 0 0 0 0 0 0 
0 1 0 0 0 0 0 0 0 0 0 
0 0 1 0 0 0 0 0 0 0 0 
0 0 0 1 0 0 0 0 0 0 0 
0 0 0 0 1 0 0 0 0 0 0 
0 0 0 0 0 1 0 0 0 0 0 
0 0 0 0 0 0 1 0 0 0 0 
0 0 0 0 0 0 0 1 0 0 0 
0 0 0 0 0 0 0 0 1 0 0 
0 0 0 0 0 0 0 0 0 1 0 
2 2 2 2 2 2 2 2 2 2 2 
, 
1 0 0 0 0 0 0 0 0 0 0 
0 0 1 0 0 0 0 0 0 0 0 
0 0 0 0 1 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 1 0 0 
0 1 0 0 0 0 0 0 0 0 0 
0 0 0 1 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 1 0 0 0 
0 0 0 0 0 0 0 0 0 1 0 
0 0 0 0 0 1 0 0 0 0 0 
0 0 0 0 0 0 1 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 1 
, 
0 0 0 0 0 0 0 0 0 2 0 
0 0 0 0 0 0 0 0 2 0 0 
0 0 0 0 0 0 1 0 0 0 0 
2 2 2 2 1 1 1 1 0 0 0 
0 1 0 0 0 0 0 0 0 0 0 
1 0 0 0 0 0 0 0 0 0 0 
1 1 2 0 1 1 2 0 2 2 0 
0 0 0 2 0 0 0 0 0 0 0 
0 0 0 0 2 0 0 0 0 0 0 
0 0 0 0 0 2 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 1 
, 
0 2 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 1 0 0 0 
1 1 2 0 1 1 2 0 2 2 0 
2 2 2 2 1 1 1 1 0 0 0 
1 2 1 2 1 0 0 2 1 2 0 
0 0 0 0 0 0 0 0 1 0 0 
0 0 0 0 0 2 0 0 0 0 0 
0 0 0 0 1 0 0 0 0 0 0 
0 0 2 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 1 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 1 
)
acting on the columns of the generator matrix as follows (in order):
(11, 12), 
(2, 5, 3)(4, 6, 9)(7, 10, 8)(13, 14, 15), 
(1, 6, 10)(2, 5, 9)(3, 14, 7)(4, 8, 13), 
(1, 13, 4, 14, 3, 9, 6, 7, 10, 15, 5, 8, 2)
orbits: { 1, 10, 2, 7, 6, 3, 9, 8, 14, 4, 5, 13, 15 }, { 11, 12 }

code no       2:
================
1 1 1 1 1 1 1 1 1 1 1 2 0 0 0
2 2 2 2 1 1 1 1 0 0 0 0 2 0 0
2 2 1 0 2 2 1 0 1 1 0 0 0 2 0
2 0 2 1 2 1 2 0 1 0 1 0 0 0 2
the automorphism group has order 36
and is strongly generated by the following 4 elements:
(
2 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 1 0 0 0 
2 2 2 2 1 1 1 1 0 0 0 
1 1 1 1 1 1 1 1 1 1 1 
2 2 1 0 2 2 1 0 1 1 0 
0 0 0 0 0 0 0 0 0 0 1 
0 0 0 0 0 0 1 0 0 0 0 
0 1 0 0 0 0 0 0 0 0 0 
2 0 2 1 2 1 2 0 1 0 1 
0 0 0 0 0 0 0 0 0 1 0 
0 0 0 0 0 1 0 0 0 0 0 
, 
2 0 0 0 0 0 0 0 0 0 0 
2 2 1 0 2 2 1 0 1 1 0 
0 0 0 0 0 0 0 0 1 0 0 
0 0 0 0 0 0 0 0 0 0 2 
0 2 0 0 0 0 0 0 0 0 0 
0 0 0 1 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 1 0 
0 0 0 0 1 0 0 0 0 0 0 
1 1 1 1 2 2 2 2 0 0 0 
0 0 0 0 0 0 2 0 0 0 0 
1 1 1 1 1 1 1 1 1 1 1 
, 
0 0 0 0 2 0 0 0 0 0 0 
0 0 0 0 0 2 0 0 0 0 0 
0 0 0 0 0 0 2 0 0 0 0 
0 0 0 0 0 0 0 2 0 0 0 
2 0 0 0 0 0 0 0 0 0 0 
0 2 0 0 0 0 0 0 0 0 0 
0 0 2 0 0 0 0 0 0 0 0 
0 0 0 2 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 2 0 
0 0 0 0 0 0 0 0 2 0 0 
1 1 1 1 1 1 1 1 1 1 1 
, 
0 0 0 0 0 0 0 0 0 0 1 
2 2 2 2 2 2 2 2 2 2 2 
1 1 1 1 2 2 2 2 0 0 0 
0 0 0 0 0 0 0 2 0 0 0 
0 2 0 0 0 0 0 0 0 0 0 
2 0 0 0 0 0 0 0 0 0 0 
0 0 1 0 0 0 0 0 0 0 0 
1 1 2 0 1 1 2 0 2 2 0 
0 0 0 0 0 0 0 0 2 0 0 
0 0 0 0 0 0 0 0 0 2 0 
0 0 0 0 0 1 0 0 0 0 0 
)
acting on the columns of the generator matrix as follows (in order):
(2, 8)(3, 13)(4, 12)(5, 14)(6, 11)(9, 15), 
(2, 5, 8, 14)(3, 15, 13, 9)(4, 6, 12, 11)(7, 10), 
(1, 5)(2, 6)(3, 7)(4, 8)(9, 10)(11, 12), 
(1, 6, 11)(2, 5, 12)(3, 7, 13)(4, 14, 8)
orbits: { 1, 5, 11, 14, 2, 6, 12, 8, 4 }, { 3, 13, 9, 7, 15, 10 }

code no       3:
================
1 1 1 1 1 1 1 1 1 1 1 2 0 0 0
2 2 2 2 1 1 1 1 0 0 0 0 2 0 0
2 2 1 0 2 2 1 0 1 1 0 0 0 2 0
1 0 2 2 1 0 2 2 1 0 1 0 0 0 2
the automorphism group has order 720
and is strongly generated by the following 4 elements:
(
2 0 0 0 0 0 0 0 0 0 0 
0 2 0 0 0 0 0 0 0 0 0 
0 0 1 0 0 0 0 0 0 0 0 
1 1 2 0 1 1 2 0 2 2 0 
2 2 2 2 2 2 2 2 2 2 2 
0 0 0 0 0 0 0 0 0 0 1 
1 1 1 1 2 2 2 2 0 0 0 
0 0 0 0 0 0 0 2 0 0 0 
0 0 0 0 0 0 0 0 2 0 0 
0 0 0 0 0 0 0 0 0 2 0 
0 0 0 0 0 1 0 0 0 0 0 
, 
1 0 0 0 0 0 0 0 0 0 0 
0 1 0 0 0 0 0 0 0 0 0 
2 2 1 0 2 2 1 0 1 1 0 
0 0 2 0 0 0 0 0 0 0 0 
1 1 1 1 1 1 1 1 1 1 1 
0 0 0 0 0 0 0 0 0 0 2 
0 0 0 0 0 0 0 1 0 0 0 
2 2 2 2 1 1 1 1 0 0 0 
0 0 0 0 0 2 0 0 0 0 0 
0 0 0 0 2 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 1 0 0 
, 
1 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 2 0 
0 0 0 0 0 2 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 1 
0 1 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 2 0 0 
0 0 0 0 2 0 0 0 0 0 0 
2 2 2 2 2 2 2 2 2 2 2 
1 1 2 0 1 1 2 0 2 2 0 
0 0 0 0 0 0 1 0 0 0 0 
0 0 0 2 0 0 0 0 0 0 0 
, 
0 0 0 0 0 2 0 0 0 0 0 
0 0 0 0 2 0 0 0 0 0 0 
0 0 0 0 0 0 2 0 0 0 0 
0 0 0 0 0 0 0 2 0 0 0 
0 2 0 0 0 0 0 0 0 0 0 
2 0 0 0 0 0 0 0 0 0 0 
0 0 2 0 0 0 0 0 0 0 0 
0 0 0 2 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 2 0 
0 0 0 0 0 0 0 0 2 0 0 
1 1 1 1 1 1 1 1 1 1 1 
)
acting on the columns of the generator matrix as follows (in order):
(4, 14)(5, 12)(6, 11)(7, 13), 
(3, 4, 14)(5, 10, 12)(6, 9, 11)(7, 13, 8), 
(2, 5, 7, 10)(3, 14, 9, 6)(4, 11)(8, 15, 13, 12), 
(1, 6)(2, 5)(3, 7)(4, 8)(9, 10)(11, 12)
orbits: { 1, 6, 11, 9, 4, 12, 14, 10, 3, 8, 5, 13, 7, 2, 15 }