the 1 isometry classes of irreducible [13,3,9]_3 codes are:

code no       1:
================
1 1 1 1 1 1 1 1 0 0 2 0 0
2 2 2 1 1 1 0 0 1 1 0 2 0
2 1 0 2 1 0 2 1 2 1 0 0 2
the automorphism group has order 5616
and is strongly generated by the following 8 elements:
(
2 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 0 0 0 0 
0 0 0 1 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 0 
1 1 1 2 2 2 0 0 2 2 
0 0 0 0 0 0 0 0 0 1 
2 2 2 2 2 2 2 2 0 0 
0 0 0 0 0 0 0 1 0 0 
, 
2 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 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 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 0 0 0 0 1 0 0 
0 0 0 0 0 0 1 0 0 0 
, 
2 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 0 0 0 0 
0 0 0 0 0 0 0 2 0 0 
1 1 1 1 1 1 1 1 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 2 0 0 0 0 0 0 
1 1 1 2 2 2 0 0 2 2 
0 0 0 0 0 0 0 0 0 1 
, 
2 0 0 0 0 0 0 0 0 0 
0 1 0 0 0 0 0 0 0 0 
1 2 0 1 2 0 1 2 1 2 
0 0 0 0 0 0 0 0 0 1 
0 0 0 2 0 0 0 0 0 0 
0 0 0 0 0 0 0 1 0 0 
0 0 0 0 1 0 0 0 0 0 
0 0 0 0 0 0 0 0 2 0 
0 0 0 0 0 1 0 0 0 0 
2 2 2 1 1 1 0 0 1 1 
, 
2 0 0 0 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 0 0 0 0 0 0 0 1 
1 1 1 2 2 2 0 0 2 2 
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 1 0 0 0 0 
0 0 0 0 0 0 0 2 0 0 
0 0 0 0 0 0 2 0 0 0 
, 
2 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 2 0 0 0 
0 0 0 2 0 0 0 0 0 0 
2 1 0 2 1 0 2 1 2 1 
0 0 0 0 0 0 0 0 0 2 
0 0 0 0 0 0 0 0 1 0 
0 0 1 0 0 0 0 0 0 0 
0 0 0 0 0 1 0 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 1 0 0 0 0 0 
0 0 0 0 0 1 0 0 0 0 
0 0 0 1 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 0 
0 2 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 1 
1 1 1 2 2 2 0 0 2 2 
0 0 0 0 0 0 0 2 0 0 
0 0 0 0 0 0 2 0 0 0 
, 
2 1 0 2 1 0 2 1 2 1 
0 0 0 0 0 2 0 0 0 0 
0 0 0 0 1 0 0 0 0 0 
0 0 0 0 0 0 0 0 2 0 
0 2 0 0 0 0 0 0 0 0 
2 2 2 2 2 2 2 2 0 0 
1 1 1 2 2 2 0 0 2 2 
0 0 0 0 0 0 2 0 0 0 
0 0 0 0 0 0 0 2 0 0 
0 0 1 0 0 0 0 0 0 0 
)
acting on the columns of the generator matrix as follows (in order):
(5, 6)(7, 12)(8, 10)(9, 11), 
(4, 5)(7, 10)(8, 9)(11, 12), 
(4, 8)(5, 11)(6, 7)(9, 12), 
(3, 13)(4, 5, 7, 11, 12, 10)(6, 9, 8), 
(2, 3)(4, 11, 12, 5, 7, 10)(6, 8, 9), 
(2, 12, 13, 4, 3, 7)(5, 10)(6, 8, 9), 
(1, 4, 3, 5)(2, 6)(7, 10)(8, 9, 11, 12), 
(1, 11, 6, 2, 5, 3, 10, 12, 7, 8, 9, 4, 13)
orbits: { 1, 5, 13, 6, 4, 11, 12, 10, 3, 2, 7, 8, 9 }