the 6 isometry classes of irreducible [6,3,4]_9 codes are:

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

code no       2:
================
1 1 1 2 0 0
3 2 1 0 2 0
6 3 1 0 0 2
the automorphism group has order 48
and is strongly generated by the following 4 elements:
(
8 0 0 
0 3 0 
1 3 6 
, 1
, 
8 0 0 
4 4 4 
0 0 8 
, 1
, 
6 0 0 
4 1 2 
2 2 2 
, 1
, 
2 4 8 
2 1 4 
0 7 0 
, 0
)
acting on the columns of the generator matrix as follows (in order):
(3, 5), 
(2, 4), 
(2, 5)(3, 4), 
(1, 4, 5)(2, 3, 6)
orbits: { 1, 5, 3, 2, 4, 6 }

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

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

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

code no       6:
================
1 1 1 2 0 0
4 3 1 0 2 0
5 4 1 0 0 2
the automorphism group has order 120
and is strongly generated by the following 7 elements:
(
4 0 0 
0 4 0 
3 7 8 
, 0
, 
6 0 0 
0 8 0 
1 1 1 
, 1
, 
8 0 0 
0 0 3 
5 5 5 
, 1
, 
6 0 0 
4 1 3 
2 2 2 
, 0
, 
0 4 0 
8 8 8 
4 0 0 
, 1
, 
1 5 8 
7 0 0 
0 3 0 
, 1
, 
2 6 5 
0 0 6 
1 1 1 
, 0
)
acting on the columns of the generator matrix as follows (in order):
(3, 6)(4, 5), 
(3, 5, 6, 4), 
(2, 5, 4, 3), 
(2, 6)(3, 4), 
(1, 3, 4, 2), 
(1, 2, 3, 5), 
(1, 5, 6)(2, 4, 3)
orbits: { 1, 2, 5, 6, 3, 4 }