the 2 isometry classes of irreducible [9,5,5]_9 codes are:

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

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