the 2 isometry classes of irreducible [6,2,4]_3 codes are:

code no       1:
================
1 1 1 1 2 0
2 1 1 0 0 2
the automorphism group has order 16
and is strongly generated by the following 4 elements:
(
2 0 0 0 
0 2 0 0 
0 0 2 0 
1 1 1 1 
, 
1 0 0 0 
0 0 1 0 
0 1 0 0 
0 0 0 1 
, 
1 0 0 0 
2 2 2 2 
0 0 0 1 
0 1 0 0 
, 
2 1 1 0 
0 0 0 2 
1 1 1 1 
0 1 0 0 
)
acting on the columns of the generator matrix as follows (in order):
(4, 5), 
(2, 3), 
(2, 4, 3, 5), 
(1, 6)(2, 4)(3, 5)
orbits: { 1, 6 }, { 2, 3, 5, 4 }

code no       2:
================
1 1 1 0 2 0
1 1 0 1 0 2
the automorphism group has order 48
and is strongly generated by the following 5 elements:
(
2 0 0 0 
0 2 0 0 
0 0 2 0 
1 1 0 1 
, 
2 0 0 0 
0 2 0 0 
1 1 1 0 
0 0 0 2 
, 
2 0 0 0 
0 2 0 0 
0 0 0 2 
0 0 2 0 
, 
2 2 2 0 
0 0 1 0 
0 1 0 0 
0 0 0 2 
, 
1 1 0 1 
0 0 0 2 
0 2 0 0 
2 2 2 0 
)
acting on the columns of the generator matrix as follows (in order):
(4, 6), 
(3, 5), 
(3, 4)(5, 6), 
(1, 5)(2, 3), 
(1, 5, 4, 2, 3, 6)
orbits: { 1, 5, 6, 3, 4, 2 }