the 3 isometry classes of irreducible [13,2,9]_3 codes are:

code no       1:
================
1 1 1 1 1 1 1 1 1 1 1 2 0
2 2 2 2 1 1 1 1 0 0 0 0 2
the automorphism group has order 82944
and is strongly generated by the following 12 elements:
(
1 0 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 
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 1 0 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 0 0 0 1 0 0 
0 0 0 0 0 0 0 0 0 1 0 
2 2 2 2 2 2 2 2 2 2 2 
, 
2 0 0 0 0 0 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 
0 0 0 2 0 0 0 0 0 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 0 0 0 2 0 0 0 0 
0 0 0 0 0 0 0 2 0 0 0 
0 0 0 0 0 0 0 0 2 0 0 
1 1 1 1 1 1 1 1 1 1 1 
0 0 0 0 0 0 0 0 0 2 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 1 0 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 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 1 0 0 0 
2 2 2 2 2 2 2 2 2 2 2 
0 0 0 0 0 0 0 0 0 1 0 
0 0 0 0 0 0 0 0 1 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 1 0 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 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 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 1 
0 0 0 0 0 0 0 0 1 0 0 
, 
2 0 0 0 0 0 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 
0 0 0 2 0 0 0 0 0 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 0 0 0 0 2 0 0 0 
0 0 0 0 0 0 2 0 0 0 0 
1 1 1 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 0 0 0 0 2 
, 
1 0 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 
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 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 1 0 
0 0 0 0 0 0 0 0 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 0 2 0 0 0 0 0 0 0 0 
0 0 0 2 0 0 0 0 0 0 0 
1 1 1 1 1 1 1 1 1 1 1 
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 2 0 
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 
, 
1 0 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 
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 1 0 0 0 0 0 0 
0 0 0 0 0 0 0 1 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 0 0 0 1 
0 0 0 0 0 0 0 0 1 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 1 0 0 0 0 0 0 0 
0 0 1 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 1 0 
0 0 0 0 0 0 0 0 1 0 0 
2 2 2 2 2 2 2 2 2 2 2 
0 0 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 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 0 0 2 0 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 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 0 0 0 0 0 2 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 0 0 0 0 0 0 0 2 0 
1 1 1 1 1 1 1 1 1 1 1 
, 
2 0 0 0 0 0 0 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 2 0 0 0 0 0 
0 0 0 0 2 0 0 0 0 0 0 
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 0 0 0 0 2 0 
1 1 1 1 1 1 1 1 1 1 1 
0 0 0 0 0 0 0 0 0 0 2 
, 
0 0 0 0 0 2 0 0 0 0 0 
0 0 0 0 2 0 0 0 0 0 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 2 0 0 0 0 0 0 0 0 
0 0 0 2 0 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 0 
0 0 0 0 0 0 0 0 0 2 0 
0 0 0 0 0 0 0 0 0 0 2 
1 1 1 1 1 1 1 1 1 1 1 
)
acting on the columns of the generator matrix as follows (in order):
(11, 12), 
(10, 11, 12), 
(9, 11, 12), 
(9, 11, 10), 
(7, 8)(9, 10, 12), 
(6, 7, 8), 
(5, 12)(6, 11)(7, 9)(8, 10), 
(5, 6)(7, 8)(9, 11, 10), 
(3, 4)(5, 11, 8, 12, 7, 10)(6, 9), 
(2, 4)(5, 6)(7, 8)(9, 12, 11), 
(2, 4, 3)(5, 6)(9, 12, 10), 
(1, 7, 4, 6)(2, 8, 3, 5)(9, 12, 11, 10)
orbits: { 1, 6, 8, 11, 5, 9, 4, 7, 10, 2, 12, 3 }, { 13 }

code no       2:
================
1 1 1 1 1 1 1 1 0 0 0 2 0
2 2 1 1 1 0 0 0 1 1 1 0 2
the automorphism group has order 13824
and is strongly generated by the following 11 elements:
(
1 0 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 
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 1 0 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 0 0 0 1 0 0 
0 0 0 0 0 0 0 0 0 1 0 
1 1 2 2 2 0 0 0 2 2 2 
, 
1 0 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 
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 1 0 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 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 1 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 1 0 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 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 1 0 0 0 
0 0 0 0 0 0 0 0 0 0 1 
0 0 0 0 0 0 0 0 0 1 0 
0 0 0 0 0 0 0 0 1 0 0 
, 
2 0 0 0 0 0 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 
0 0 0 2 0 0 0 0 0 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 0 0 0 2 0 0 0 0 
0 0 0 0 0 0 0 2 0 0 0 
2 2 1 1 1 0 0 0 1 1 1 
0 0 0 0 0 0 0 0 2 0 0 
0 0 0 0 0 0 0 0 0 0 2 
, 
2 0 0 0 0 0 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 
0 0 0 2 0 0 0 0 0 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 0 0 0 2 0 0 0 0 
1 1 1 1 1 1 1 1 0 0 0 
0 0 0 0 0 0 0 0 2 0 0 
0 0 0 0 0 0 0 0 0 0 2 
0 0 0 0 0 0 0 0 0 2 0 
, 
2 0 0 0 0 0 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 
0 0 0 2 0 0 0 0 0 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 0 0 0 0 2 0 0 0 
0 0 0 0 0 0 2 0 0 0 0 
0 0 0 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 
, 
1 0 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 
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 1 0 0 0 0 
0 0 0 0 0 1 0 0 0 0 0 
2 2 2 2 2 2 2 2 0 0 0 
0 0 0 0 0 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 1 0 
, 
2 0 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 
0 0 0 1 0 0 0 0 0 0 0 
0 0 0 0 1 0 0 0 0 0 0 
1 1 2 2 2 0 0 0 2 2 2 
0 0 0 0 0 0 0 0 0 0 1 
0 0 0 0 0 0 0 0 1 0 0 
2 2 2 2 2 2 2 2 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 
, 
2 0 0 0 0 0 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 
0 0 0 0 2 0 0 0 0 0 0 
0 0 0 2 0 0 0 0 0 0 0 
0 0 0 0 0 0 2 0 0 0 0 
0 0 0 0 0 0 0 2 0 0 0 
1 1 1 1 1 1 1 1 0 0 0 
0 0 0 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 
, 
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 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 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 
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 1 0 0 0 0 0 0 0 0 0 
1 0 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 
0 0 0 1 0 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 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 0 0 0 1 
0 0 0 0 0 0 0 0 1 0 0 
)
acting on the columns of the generator matrix as follows (in order):
(11, 13), 
(10, 11), 
(9, 11), 
(9, 10, 13), 
(8, 12)(10, 11), 
(7, 8)(9, 11, 10), 
(6, 7)(8, 12)(10, 11), 
(6, 11, 7, 13)(8, 10, 12, 9), 
(4, 5)(6, 12, 8, 7)(9, 11, 10), 
(3, 5, 4)(6, 8, 7)(9, 10, 11), 
(1, 2)(3, 4, 5)(6, 7, 8)(9, 11, 10)
orbits: { 1, 2 }, { 3, 4, 5 }, { 6, 7, 13, 8, 11, 10, 12, 9 }

code no       3:
================
1 1 1 1 1 1 1 1 0 0 0 2 0
2 2 2 1 1 1 0 0 1 1 1 0 2
the automorphism group has order 31104
and is strongly generated by the following 11 elements:
(
2 0 0 0 0 0 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 
0 0 0 2 0 0 0 0 0 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 0 0 0 2 0 0 0 0 
0 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 0 0 0 2 0 
2 2 2 1 1 1 0 0 1 1 1 
, 
2 0 0 0 0 0 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 
0 0 0 2 0 0 0 0 0 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 0 0 0 2 0 0 0 0 
0 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 0 0 0 0 2 
0 0 0 0 0 0 0 0 0 2 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 1 0 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 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 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 1 
0 0 0 0 0 0 0 0 1 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 1 0 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 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 1 0 0 0 
1 1 1 2 2 2 0 0 2 2 2 
0 0 0 0 0 0 0 0 0 0 1 
0 0 0 0 0 0 0 0 0 1 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 1 0 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 0 0 0 1 0 0 0 0 0 
0 0 0 0 0 0 1 0 0 0 0 
2 2 2 2 2 2 2 2 0 0 0 
0 0 0 0 0 0 0 0 0 0 1 
0 0 0 0 0 0 0 0 0 1 0 
0 0 0 0 0 0 0 0 1 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 1 0 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 0 0 0 1 0 0 0 0 0 
2 2 2 2 2 2 2 2 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 0 1 0 
0 0 0 0 0 0 0 0 1 0 0 
, 
2 0 0 0 0 0 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 
0 0 0 2 0 0 0 0 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 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 0 0 0 2 0 0 
0 0 0 0 0 0 0 0 0 0 2 
0 0 0 0 0 0 0 0 0 2 0 
, 
2 0 0 0 0 0 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 
1 1 1 1 1 1 1 1 0 0 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 0 2 0 0 0 0 0 
0 0 0 0 2 0 0 0 0 0 0 
0 0 0 0 0 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 1 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 1 0 0 0 0 0 0 0 0 
0 0 0 0 1 0 0 0 0 0 0 
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 1 0 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 0 0 0 0 1 
0 0 0 0 0 0 0 0 0 1 0 
, 
1 0 0 0 0 0 0 0 0 0 0 
0 0 1 0 0 0 0 0 0 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 0 1 0 0 0 0 0 
0 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 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 0 0 0 1 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 1 0 0 0 0 0 0 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 
2 2 2 2 2 2 2 2 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 0 0 0 2 0 
0 0 0 0 0 0 0 0 0 0 2 
)
acting on the columns of the generator matrix as follows (in order):
(11, 13), 
(10, 11), 
(9, 11, 10), 
(9, 13)(10, 11), 
(8, 12)(9, 11), 
(7, 12)(9, 11), 
(5, 6)(10, 11), 
(4, 12)(5, 8)(6, 7)(10, 11), 
(4, 5)(10, 11), 
(2, 3)(5, 6)(9, 10, 11), 
(1, 5, 3, 6)(2, 4)(7, 12)
orbits: { 1, 6, 5, 7, 3, 8, 4, 12, 2 }, { 9, 10, 13, 11 }