the 1 isometry classes of irreducible [13,1,13]_2 codes are:

code no       1:
================
1 1 1 1 1 1 1 1 1 1 1 1 1
the automorphism group has order 6227020800
and is strongly generated by the following 17 elements:
(
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 
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 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 0 0 0 1 0 0 
0 0 0 0 0 0 0 0 0 0 1 0 
1 1 1 1 1 1 1 1 1 1 1 1 
, 
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 
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 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 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 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 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 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 0 0 0 1 0 0 0 
0 0 0 0 0 0 0 0 0 1 0 0 
1 1 1 1 1 1 1 1 1 1 1 1 
0 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 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 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 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 1 0 0 
0 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 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 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 0 0 0 1 0 0 0 
1 1 1 1 1 1 1 1 1 1 1 1 
0 0 0 0 0 0 0 0 0 0 1 0 
0 0 0 0 0 0 0 0 0 1 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 
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 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 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 0 1 
, 
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 
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 0 0 0 1 0 0 0 0 0 
0 0 0 0 0 0 0 1 0 0 0 0 
1 1 1 1 1 1 1 1 1 1 1 1 
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 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 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 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 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 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 
, 
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 
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 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 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 0 0 0 0 1 
, 
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 
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 
1 1 1 1 1 1 1 1 1 1 1 1 
0 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 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 1 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 
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 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 0 0 0 1 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 0 1 0 
0 0 0 0 0 0 0 0 0 0 0 1 
, 
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 
0 0 0 1 0 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 0 1 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 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 0 1 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 1 
, 
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 
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 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 1 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 0 0 0 1 0 
0 0 0 0 0 0 0 0 0 0 0 1 
, 
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 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 1 0 0 0 0 0 
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 1 0 0 0 0 0 0 0 0 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 0 0 0 0 1 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 1 
, 
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 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 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 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 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 0 0 1 
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 0 0 0 0 0 0 1 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 
1 0 0 0 0 0 0 0 0 0 0 0 
0 0 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 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 
, 
1 1 1 1 1 1 1 1 1 1 1 1 
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 1 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 1 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 0 0 0 0 0 1 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 1 
0 1 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 1 0 0 0 0 
)
acting on the columns of the generator matrix as follows (in order):
(12, 13), 
(11, 12), 
(11, 12, 13), 
(10, 11, 12), 
(10, 12, 13), 
(9, 10, 11), 
(9, 12, 11, 10, 13), 
(8, 11, 12), 
(7, 10, 9), 
(7, 12, 13)(8, 11)(9, 10), 
(6, 10, 8), 
(5, 7, 10, 6, 9, 11), 
(4, 5, 10)(6, 9, 7, 8), 
(3, 8, 11, 6)(4, 10, 9)(5, 7), 
(2, 6, 4), 
(1, 7, 6, 12)(2, 11, 8, 3, 9)(4, 5, 10), 
(1, 7, 4, 8, 12, 10, 3, 5, 13)(2, 11, 6)
orbits: { 1, 12, 13, 11, 10, 9, 7, 6, 8, 5, 2, 4, 3 }