the 3 isometry classes of irreducible [7,3,5]_9 codes are:

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

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

code no       3:
================
1 1 1 1 2 0 0
8 3 2 1 0 2 0
2 6 4 1 0 0 2
the automorphism group has order 42
and is strongly generated by the following 4 elements:
(
4 0 0 0 
0 0 5 0 
6 4 1 2 
2 4 6 1 
, 1
, 
0 0 5 0 
1 1 1 1 
2 7 6 3 
0 4 0 0 
, 0
, 
0 0 0 3 
5 1 3 6 
0 2 0 0 
0 0 6 0 
, 1
, 
1 3 8 2 
4 4 4 4 
6 0 0 0 
0 0 6 0 
, 0
)
acting on the columns of the generator matrix as follows (in order):
(2, 5, 7, 4, 6, 3), 
(1, 6, 3)(2, 4, 5), 
(1, 5, 6, 2, 3, 4), 
(1, 3, 4, 6, 5, 2, 7)
orbits: { 1, 3, 4, 7, 6, 2, 5 }