the 2 isometry classes of irreducible [9,3,7]_8 codes are:

code no       1:
================
1 1 1 1 1 1 1 0 0
6 5 4 3 2 1 0 1 0
4 7 2 5 3 1 0 0 1
the automorphism group has order 168
and is strongly generated by the following 4 elements:
(
3 0 0 0 0 0 
0 3 0 0 0 0 
2 4 1 6 3 5 
1 7 3 4 6 5 
0 0 0 0 5 0 
0 0 0 2 0 0 
, 2
, 
2 0 0 0 0 0 
4 4 4 4 4 4 
6 2 7 4 1 5 
0 0 3 0 0 0 
0 0 0 0 5 0 
0 6 0 0 0 0 
, 1
, 
1 0 0 0 0 0 
2 3 6 5 1 7 
3 3 3 3 3 3 
0 0 0 6 0 0 
0 0 0 0 2 0 
0 0 5 0 0 0 
, 2
, 
0 7 0 0 0 0 
0 0 0 1 0 0 
0 0 2 0 0 0 
3 0 0 0 0 0 
0 0 0 0 4 0 
5 5 5 5 5 5 
, 1
)
acting on the columns of the generator matrix as follows (in order):
(3, 7, 8)(4, 6, 9), 
(2, 6, 7)(3, 4, 8), 
(2, 8, 9)(3, 6, 7), 
(1, 4, 2)(6, 8, 7)
orbits: { 1, 2, 7, 9, 4, 3, 6, 8 }, { 5 }

code no       2:
================
1 1 1 1 1 1 1 0 0
6 5 4 3 2 1 0 1 0
3 2 5 4 7 1 0 0 1
the automorphism group has order 1512
and is strongly generated by the following 6 elements:
(
2 0 0 0 0 0 
0 6 0 0 0 0 
0 0 3 0 0 0 
6 2 7 4 1 5 
0 0 0 0 0 1 
4 4 4 4 4 4 
, 1
, 
2 0 0 0 0 0 
0 7 0 0 0 0 
3 3 3 3 3 3 
0 0 0 0 0 4 
0 0 0 6 0 0 
0 0 0 0 1 0 
, 1
, 
4 0 0 0 0 0 
0 0 0 4 0 0 
0 0 0 0 4 0 
4 4 4 4 4 4 
0 0 0 0 0 4 
0 0 4 0 0 0 
, 1
, 
4 0 0 0 0 0 
2 6 1 5 7 4 
0 0 0 0 0 6 
0 6 0 0 0 0 
0 0 0 0 3 0 
5 3 2 6 7 1 
, 1
, 
0 6 0 0 0 0 
0 0 0 6 0 0 
0 0 0 0 0 6 
0 0 0 0 6 0 
6 6 6 6 6 6 
6 0 0 0 0 0 
, 0
, 
5 2 4 3 6 7 
1 0 0 0 0 0 
1 1 1 1 1 1 
0 0 7 0 0 0 
0 0 0 4 0 0 
5 3 2 6 7 1 
, 1
)
acting on the columns of the generator matrix as follows (in order):
(4, 9, 8)(5, 7, 6), 
(3, 8, 7)(4, 5, 6), 
(2, 7, 4)(3, 6, 5), 
(2, 4, 9)(3, 8, 6), 
(1, 6, 3, 7, 5, 4, 2), 
(1, 2, 8, 6, 7, 3, 4, 5, 9)
orbits: { 1, 2, 9, 4, 5, 8, 6, 7, 3 }