the 3 isometry classes of irreducible [7,4,4]_9 codes are:

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

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

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