the 2 isometry classes of irreducible [6,2,5]_9 codes are:

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

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