the 9 isometry classes of irreducible [6,3,3]_5 codes are:

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

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

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

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

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

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

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

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

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