the 1 isometry classes of irreducible [13,10,3]_3 codes are:

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