the 2 isometry classes of irreducible [9,4,6]_9 codes are:

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

code no       2:
================
1 1 1 1 1 2 0 0 0
5 4 3 2 1 0 2 0 0
8 5 6 4 1 0 0 2 0
6 8 2 7 1 0 0 0 2
the automorphism group has order 72
and is strongly generated by the following 3 elements:
(
1 0 0 0 0 
1 1 1 1 1 
6 1 5 4 8 
0 0 0 0 1 
4 1 6 8 5 
, 1
, 
2 2 2 2 2 
2 0 0 0 0 
0 0 0 0 2 
3 2 7 8 4 
0 0 0 1 0 
, 1
, 
2 5 3 8 6 
3 7 4 6 1 
0 0 7 0 0 
0 0 0 0 7 
7 7 7 7 7 
, 1
)
acting on the columns of the generator matrix as follows (in order):
(2, 9, 7, 3, 8, 5, 4, 6), 
(1, 2, 7, 4, 5, 3, 8, 6), 
(1, 7, 8, 2, 6, 5, 4, 9)
orbits: { 1, 6, 9, 4, 8, 2, 5, 7, 3 }