the 1 isometry classes of irreducible [9,1,9]_4 codes are:

code no       1:
================
1 1 1 1 1 1 1 1 1
the automorphism group has order 725760
and is strongly generated by the following 15 elements:
(
1 0 0 0 0 0 0 0 
0 1 0 0 0 0 0 0 
0 0 1 0 0 0 0 0 
0 0 0 1 0 0 0 0 
0 0 0 0 1 0 0 0 
0 0 0 0 0 1 0 0 
0 0 0 0 0 0 1 0 
0 0 0 0 0 0 0 1 
, 1
, 
1 0 0 0 0 0 0 0 
0 1 0 0 0 0 0 0 
0 0 1 0 0 0 0 0 
0 0 0 1 0 0 0 0 
0 0 0 0 1 0 0 0 
0 0 0 0 0 1 0 0 
0 0 0 0 0 0 1 0 
1 1 1 1 1 1 1 1 
, 0
, 
3 0 0 0 0 0 0 0 
0 3 0 0 0 0 0 0 
0 0 3 0 0 0 0 0 
0 0 0 3 0 0 0 0 
0 0 0 0 3 0 0 0 
0 0 0 0 0 3 0 0 
0 0 0 0 0 0 0 3 
0 0 0 0 0 0 3 0 
, 1
, 
1 0 0 0 0 0 0 0 
0 1 0 0 0 0 0 0 
0 0 1 0 0 0 0 0 
0 0 0 1 0 0 0 0 
0 0 0 0 1 0 0 0 
0 0 0 0 0 1 0 0 
1 1 1 1 1 1 1 1 
0 0 0 0 0 0 0 1 
, 0
, 
2 0 0 0 0 0 0 0 
0 2 0 0 0 0 0 0 
0 0 2 0 0 0 0 0 
0 0 0 2 0 0 0 0 
0 0 0 0 2 0 0 0 
0 0 0 0 0 0 2 0 
0 0 0 0 0 0 0 2 
0 0 0 0 0 2 0 0 
, 0
, 
2 0 0 0 0 0 0 0 
0 2 0 0 0 0 0 0 
0 0 2 0 0 0 0 0 
0 0 0 2 0 0 0 0 
0 0 0 0 0 0 2 0 
0 0 0 0 0 2 0 0 
0 0 0 0 0 0 0 2 
0 0 0 0 2 0 0 0 
, 1
, 
3 0 0 0 0 0 0 0 
0 3 0 0 0 0 0 0 
0 0 3 0 0 0 0 0 
0 0 0 3 0 0 0 0 
3 3 3 3 3 3 3 3 
0 0 0 0 0 0 3 0 
0 0 0 0 3 0 0 0 
0 0 0 0 0 3 0 0 
, 0
, 
3 0 0 0 0 0 0 0 
0 3 0 0 0 0 0 0 
0 0 3 0 0 0 0 0 
0 0 0 0 3 0 0 0 
0 0 0 0 0 0 0 3 
0 0 0 0 0 0 3 0 
0 0 0 3 0 0 0 0 
0 0 0 0 0 3 0 0 
, 1
, 
3 0 0 0 0 0 0 0 
0 3 0 0 0 0 0 0 
0 0 0 0 0 3 0 0 
0 0 0 0 3 0 0 0 
0 0 0 3 0 0 0 0 
0 0 3 0 0 0 0 0 
0 0 0 0 0 0 3 0 
0 0 0 0 0 0 0 3 
, 1
, 
3 0 0 0 0 0 0 0 
0 3 0 0 0 0 0 0 
0 0 0 0 0 0 0 3 
0 0 0 3 0 0 0 0 
0 0 3 0 0 0 0 0 
0 0 0 0 0 0 3 0 
0 0 0 0 0 3 0 0 
0 0 0 0 3 0 0 0 
, 0
, 
1 0 0 0 0 0 0 0 
0 0 0 0 0 0 1 0 
0 0 0 0 0 0 0 1 
0 0 0 0 1 0 0 0 
0 0 1 0 0 0 0 0 
0 0 0 1 0 0 0 0 
0 1 0 0 0 0 0 0 
0 0 0 0 0 1 0 0 
, 1
, 
2 0 0 0 0 0 0 0 
0 0 0 0 2 0 0 0 
0 0 0 0 0 0 0 2 
0 0 0 2 0 0 0 0 
0 0 2 0 0 0 0 0 
0 0 0 0 0 0 2 0 
0 0 0 0 0 2 0 0 
0 2 0 0 0 0 0 0 
, 0
, 
3 0 0 0 0 0 0 0 
3 3 3 3 3 3 3 3 
0 0 0 0 0 0 0 3 
0 3 0 0 0 0 0 0 
0 0 0 0 3 0 0 0 
0 0 0 0 0 3 0 0 
0 0 0 3 0 0 0 0 
0 0 3 0 0 0 0 0 
, 0
, 
0 0 0 0 2 0 0 0 
0 0 0 0 0 0 0 2 
2 0 0 0 0 0 0 0 
0 0 0 0 0 0 2 0 
0 0 0 2 0 0 0 0 
0 0 2 0 0 0 0 0 
0 2 0 0 0 0 0 0 
0 0 0 0 0 2 0 0 
, 1
, 
3 3 3 3 3 3 3 3 
0 0 0 0 0 0 3 0 
0 0 0 3 0 0 0 0 
0 0 3 0 0 0 0 0 
0 3 0 0 0 0 0 0 
0 0 0 0 3 0 0 0 
3 0 0 0 0 0 0 0 
0 0 0 0 0 3 0 0 
, 0
)
acting on the columns of the generator matrix as follows (in order):
id, 
(8, 9), 
(7, 8), 
(7, 9), 
(6, 8, 7), 
(5, 8, 7), 
(5, 7, 6, 8, 9), 
(4, 7, 6, 8, 5), 
(3, 6)(4, 5), 
(3, 5, 8)(6, 7), 
(2, 7)(3, 5, 4, 6, 8), 
(2, 8, 3, 5)(6, 7), 
(2, 4, 7, 9)(3, 8), 
(1, 3, 6, 8, 2, 7, 4, 5), 
(1, 7, 2, 5, 6, 8, 9)(3, 4)
orbits: { 1, 5, 9, 7, 8, 4, 3, 2, 6 }