the 3 isometry classes of irreducible [6,3,4]_8 codes are:

code no       1:
================
1 1 1 1 0 0
3 2 1 0 1 0
2 3 1 0 0 1
the automorphism group has order 24
and is strongly generated by the following 5 elements:
(
3 0 0 
0 3 0 
6 5 3 
, 0
, 
4 0 0 
0 4 0 
4 4 4 
, 0
, 
2 2 2 
0 0 2 
0 2 0 
, 0
, 
0 7 0 
7 0 0 
7 7 7 
, 0
, 
2 3 1 
3 2 1 
0 0 1 
, 0
)
acting on the columns of the generator matrix as follows (in order):
(3, 6)(4, 5), 
(3, 4)(5, 6), 
(1, 4)(2, 3), 
(1, 2)(3, 4), 
(1, 6)(2, 5)
orbits: { 1, 4, 2, 6, 5, 3 }

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

code no       3:
================
1 1 1 1 0 0
3 2 1 0 1 0
7 3 1 0 0 1
the automorphism group has order 18
and is strongly generated by the following 3 elements:
(
6 0 0 
0 3 0 
0 0 5 
, 2
, 
0 0 1 
1 0 0 
0 1 0 
, 2
, 
1 6 7 
4 4 4 
6 2 3 
, 2
)
acting on the columns of the generator matrix as follows (in order):
(4, 6, 5), 
(1, 2, 3), 
(1, 4, 2, 6, 3, 5)
orbits: { 1, 3, 5, 2, 6, 4 }