the 1 isometry classes of irreducible [6,3,3]_2 codes are:

code no       1:
================
1 1 1 1 0 0
1 1 0 0 1 0
1 0 1 0 0 1
the automorphism group has order 24
and is strongly generated by the following 5 elements:
(
1 0 0 
0 0 1 
0 1 0 
, 
1 0 0 
1 1 0 
1 0 1 
, 
0 1 0 
1 0 0 
1 1 1 
, 
0 0 1 
1 1 1 
1 0 0 
, 
1 0 1 
1 0 0 
1 1 1 
)
acting on the columns of the generator matrix as follows (in order):
(2, 3)(5, 6), 
(2, 5)(3, 6), 
(1, 2)(3, 4), 
(1, 3)(2, 4), 
(1, 2, 6)(3, 5, 4)
orbits: { 1, 2, 3, 6, 5, 4 }