the 5 isometry classes of irreducible [9,2,6]_4 codes are:

code no       1:
================
1 1 1 1 1 1 1 1 0
2 2 1 1 1 0 0 0 1
the automorphism group has order 144
and is strongly generated by the following 7 elements:
(
2 0 0 0 0 0 0 
0 2 0 0 0 0 0 
0 0 2 0 0 0 0 
0 0 0 2 0 0 0 
0 0 0 0 2 0 0 
0 0 0 0 0 2 0 
2 2 2 2 2 2 2 
, 0
, 
2 0 0 0 0 0 0 
0 2 0 0 0 0 0 
0 0 2 0 0 0 0 
0 0 0 2 0 0 0 
0 0 0 0 2 0 0 
2 2 2 2 2 2 2 
0 0 0 0 0 0 2 
, 0
, 
1 0 0 0 0 0 0 
0 1 0 0 0 0 0 
0 0 1 0 0 0 0 
0 0 0 1 0 0 0 
0 0 0 0 1 0 0 
0 0 0 0 0 0 1 
0 0 0 0 0 1 0 
, 0
, 
3 0 0 0 0 0 0 
0 3 0 0 0 0 0 
0 0 3 0 0 0 0 
0 0 0 0 3 0 0 
0 0 0 3 0 0 0 
0 0 0 0 0 3 0 
0 0 0 0 0 0 3 
, 0
, 
3 0 0 0 0 0 0 
0 3 0 0 0 0 0 
0 0 0 0 3 0 0 
0 0 3 0 0 0 0 
0 0 0 3 0 0 0 
0 0 0 0 0 3 0 
0 0 0 0 0 0 3 
, 0
, 
2 0 0 0 0 0 0 
0 2 0 0 0 0 0 
2 2 2 2 2 2 2 
0 0 0 0 0 0 2 
0 0 0 0 0 2 0 
0 0 2 0 0 0 0 
0 0 0 0 2 0 0 
, 1
, 
0 3 0 0 0 0 0 
3 0 0 0 0 0 0 
0 0 3 0 0 0 0 
0 0 0 3 0 0 0 
0 0 0 0 3 0 0 
0 0 0 0 0 3 0 
0 0 0 0 0 0 3 
, 0
)
acting on the columns of the generator matrix as follows (in order):
(7, 8), 
(6, 8), 
(6, 7), 
(4, 5), 
(3, 4, 5), 
(3, 6, 5, 7, 4, 8), 
(1, 2)
orbits: { 1, 2 }, { 3, 5, 8, 4, 6, 7 }, { 9 }

code no       2:
================
1 1 1 1 1 1 1 1 0
3 2 1 1 1 0 0 0 1
the automorphism group has order 432
and is strongly generated by the following 7 elements:
(
2 0 0 0 0 0 0 
0 2 0 0 0 0 0 
0 0 2 0 0 0 0 
0 0 0 2 0 0 0 
0 0 0 0 2 0 0 
0 0 0 0 0 2 0 
2 2 2 2 2 2 2 
, 0
, 
3 0 0 0 0 0 0 
0 3 0 0 0 0 0 
0 0 3 0 0 0 0 
0 0 0 3 0 0 0 
0 0 0 0 3 0 0 
0 0 0 0 0 0 3 
0 0 0 0 0 3 0 
, 0
, 
1 0 0 0 0 0 0 
0 1 0 0 0 0 0 
0 0 1 0 0 0 0 
0 0 0 0 1 0 0 
0 0 0 1 0 0 0 
1 1 1 1 1 1 1 
0 0 0 0 0 1 0 
, 0
, 
2 0 0 0 0 0 0 
0 2 0 0 0 0 0 
0 0 0 0 0 0 2 
2 2 2 2 2 2 2 
0 0 0 0 0 2 0 
0 0 2 0 0 0 0 
0 0 0 0 2 0 0 
, 1
, 
1 0 0 0 0 0 0 
3 2 1 1 1 0 0 
0 0 0 0 0 2 0 
0 0 0 0 0 0 2 
2 2 2 2 2 2 2 
0 0 0 3 0 0 0 
0 0 0 0 3 0 0 
, 0
, 
0 2 0 0 0 0 0 
2 0 0 0 0 0 0 
0 0 0 0 2 0 0 
0 0 0 2 0 0 0 
0 0 2 0 0 0 0 
0 0 0 0 0 0 2 
2 2 2 2 2 2 2 
, 1
, 
3 1 2 2 2 0 0 
2 0 0 0 0 0 0 
1 1 1 1 1 1 1 
0 0 0 0 0 1 0 
0 0 0 0 0 0 1 
0 0 0 0 3 0 0 
0 0 3 0 0 0 0 
, 1
)
acting on the columns of the generator matrix as follows (in order):
(7, 8), 
(6, 7), 
(4, 5)(6, 7, 8), 
(3, 6, 5, 7)(4, 8), 
(2, 9)(3, 8, 5, 7, 4, 6), 
(1, 2)(3, 5)(6, 8, 7), 
(1, 2, 9)(3, 7, 5, 6, 4, 8)
orbits: { 1, 2, 9 }, { 3, 7, 6, 5, 8, 4 }

code no       3:
================
1 1 1 1 1 1 1 1 0
3 2 2 1 1 0 0 0 1
the automorphism group has order 96
and is strongly generated by the following 6 elements:
(
3 0 0 0 0 0 0 
0 3 0 0 0 0 0 
0 0 3 0 0 0 0 
0 0 0 3 0 0 0 
0 0 0 0 3 0 0 
0 0 0 0 0 3 0 
3 3 3 3 3 3 3 
, 0
, 
1 0 0 0 0 0 0 
0 1 0 0 0 0 0 
0 0 1 0 0 0 0 
0 0 0 1 0 0 0 
0 0 0 0 1 0 0 
1 1 1 1 1 1 1 
0 0 0 0 0 0 1 
, 0
, 
1 0 0 0 0 0 0 
0 1 0 0 0 0 0 
0 0 1 0 0 0 0 
0 0 0 0 1 0 0 
0 0 0 1 0 0 0 
0 0 0 0 0 0 1 
1 1 1 1 1 1 1 
, 0
, 
3 0 0 0 0 0 0 
0 0 3 0 0 0 0 
0 3 0 0 0 0 0 
0 0 0 0 3 0 0 
0 0 0 3 0 0 0 
0 0 0 0 0 3 0 
3 3 3 3 3 3 3 
, 0
, 
1 0 0 0 0 0 0 
0 0 0 1 0 0 0 
0 0 0 0 1 0 0 
0 1 0 0 0 0 0 
0 0 1 0 0 0 0 
0 0 0 0 0 1 0 
1 1 1 1 1 1 1 
, 1
, 
3 1 1 2 2 0 0 
0 0 2 0 0 0 0 
0 2 0 0 0 0 0 
0 0 0 0 1 0 0 
0 0 0 1 0 0 0 
0 0 0 0 0 3 0 
3 3 3 3 3 3 3 
, 1
)
acting on the columns of the generator matrix as follows (in order):
(7, 8), 
(6, 8), 
(4, 5)(6, 8, 7), 
(2, 3)(4, 5)(7, 8), 
(2, 4)(3, 5)(7, 8), 
(1, 9)(2, 3)(4, 5)(7, 8)
orbits: { 1, 9 }, { 2, 3, 4, 5 }, { 6, 8, 7 }

code no       4:
================
1 1 1 1 1 0 0 1 0
1 1 1 0 0 1 1 0 1
the automorphism group has order 2592
and is strongly generated by the following 10 elements:
(
2 0 0 0 0 0 0 
0 2 0 0 0 0 0 
0 0 2 0 0 0 0 
0 0 0 2 0 0 0 
0 0 0 0 2 0 0 
0 0 0 0 0 2 0 
0 0 0 0 0 0 2 
, 1
, 
2 0 0 0 0 0 0 
0 2 0 0 0 0 0 
0 0 2 0 0 0 0 
0 0 0 2 0 0 0 
0 0 0 0 2 0 0 
0 0 0 0 0 2 0 
2 2 2 0 0 2 2 
, 1
, 
3 0 0 0 0 0 0 
0 3 0 0 0 0 0 
0 0 3 0 0 0 0 
0 0 0 3 0 0 0 
0 0 0 0 3 0 0 
0 0 0 0 0 0 3 
0 0 0 0 0 3 0 
, 0
, 
1 0 0 0 0 0 0 
0 1 0 0 0 0 0 
0 0 1 0 0 0 0 
0 0 0 1 0 0 0 
0 0 0 0 1 0 0 
1 1 1 0 0 1 1 
0 0 0 0 0 1 0 
, 0
, 
3 0 0 0 0 0 0 
0 3 0 0 0 0 0 
0 0 3 0 0 0 0 
0 0 0 3 0 0 0 
3 3 3 3 3 0 0 
0 0 0 0 0 3 0 
0 0 0 0 0 0 3 
, 0
, 
1 0 0 0 0 0 0 
0 1 0 0 0 0 0 
0 0 1 0 0 0 0 
0 0 0 0 1 0 0 
0 0 0 1 0 0 0 
0 0 0 0 0 1 0 
0 0 0 0 0 0 1 
, 1
, 
1 0 0 0 0 0 0 
0 1 0 0 0 0 0 
0 0 1 0 0 0 0 
0 0 0 0 0 0 1 
1 1 1 0 0 1 1 
1 1 1 1 1 0 0 
0 0 0 0 1 0 0 
, 1
, 
1 0 0 0 0 0 0 
0 0 1 0 0 0 0 
0 1 0 0 0 0 0 
0 0 0 1 0 0 0 
0 0 0 0 1 0 0 
0 0 0 0 0 0 1 
0 0 0 0 0 1 0 
, 0
, 
0 0 0 1 0 0 0 
1 1 1 1 1 0 0 
0 0 0 0 1 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 1 
, 0
, 
1 1 1 0 0 1 1 
0 0 0 0 0 0 1 
0 0 0 0 0 1 0 
0 0 0 1 0 0 0 
1 1 1 1 1 0 0 
0 1 0 0 0 0 0 
1 0 0 0 0 0 0 
, 1
)
acting on the columns of the generator matrix as follows (in order):
id, 
(7, 9), 
(6, 7), 
(6, 7, 9), 
(5, 8), 
(4, 5), 
(4, 9, 5, 7)(6, 8), 
(2, 3)(6, 7), 
(1, 5, 3, 8, 2, 4), 
(1, 7, 2, 6, 3, 9)(5, 8)
orbits: { 1, 4, 9, 5, 7, 2, 3, 8, 6 }

code no       5:
================
1 1 1 1 1 0 0 1 0
2 2 1 1 0 1 1 0 1
the automorphism group has order 288
and is strongly generated by the following 8 elements:
(
3 0 0 0 0 0 0 
0 3 0 0 0 0 0 
0 0 3 0 0 0 0 
0 0 0 3 0 0 0 
0 0 0 0 3 0 0 
0 0 0 0 0 3 0 
1 1 3 3 0 3 3 
, 0
, 
2 0 0 0 0 0 0 
0 2 0 0 0 0 0 
0 0 2 0 0 0 0 
0 0 0 2 0 0 0 
0 0 0 0 2 0 0 
0 0 0 0 0 0 2 
0 0 0 0 0 2 0 
, 0
, 
1 0 0 0 0 0 0 
0 1 0 0 0 0 0 
0 0 1 0 0 0 0 
0 0 0 1 0 0 0 
0 0 0 0 1 0 0 
2 2 1 1 0 1 1 
0 0 0 0 0 1 0 
, 0
, 
1 0 0 0 0 0 0 
0 1 0 0 0 0 0 
0 0 1 0 0 0 0 
0 0 0 1 0 0 0 
1 1 1 1 1 0 0 
0 0 0 0 0 1 0 
0 0 0 0 0 0 1 
, 0
, 
3 0 0 0 0 0 0 
0 3 0 0 0 0 0 
3 3 3 3 3 0 0 
0 0 0 0 3 0 0 
0 0 0 3 0 0 0 
0 0 0 0 0 3 0 
0 0 0 0 0 0 3 
, 1
, 
2 0 0 0 0 0 0 
0 2 0 0 0 0 0 
0 0 0 2 0 0 0 
0 0 2 0 0 0 0 
2 2 2 2 2 0 0 
0 0 0 0 0 0 2 
0 0 0 0 0 2 0 
, 0
, 
0 0 0 3 0 0 0 
0 0 3 0 0 0 0 
0 3 0 0 0 0 0 
3 0 0 0 0 0 0 
0 0 0 0 3 0 0 
0 0 0 0 0 1 0 
0 0 0 0 0 0 1 
, 1
, 
0 3 0 0 0 0 0 
3 0 0 0 0 0 0 
0 0 0 0 3 0 0 
3 3 3 3 3 0 0 
0 0 0 3 0 0 0 
0 0 0 0 0 3 0 
0 0 0 0 0 0 3 
, 1
)
acting on the columns of the generator matrix as follows (in order):
(7, 9), 
(6, 7), 
(6, 7, 9), 
(5, 8), 
(3, 8)(4, 5), 
(3, 4)(5, 8)(6, 7), 
(1, 4)(2, 3), 
(1, 2)(3, 8, 4, 5)
orbits: { 1, 4, 2, 5, 3, 8 }, { 6, 7, 9 }