the 36 isometry classes of irreducible [12,7,5]_5 codes are:

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

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

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

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

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

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

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

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

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

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

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

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

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

code no      14:
================
1 1 1 1 1 4 0 0 0 0 0 0
2 2 1 1 0 0 4 0 0 0 0 0
3 1 2 1 0 0 0 4 0 0 0 0
3 2 1 0 1 0 0 0 4 0 0 0
2 4 0 1 1 0 0 0 0 4 0 0
0 2 3 1 1 0 0 0 0 0 4 0
2 0 1 4 1 0 0 0 0 0 0 4
the automorphism group has order 1
and is strongly generated by the following 0 elements:
(
)
acting on the columns of the generator matrix as follows (in order):
orbits: { 1 }, { 2 }, { 3 }, { 4 }, { 5 }, { 6 }, { 7 }, { 8 }, { 9 }, { 10 }, { 11 }, { 12 }

code no      15:
================
1 1 1 1 1 4 0 0 0 0 0 0
2 2 1 1 0 0 4 0 0 0 0 0
3 1 2 1 0 0 0 4 0 0 0 0
3 2 1 0 1 0 0 0 4 0 0 0
0 2 3 1 1 0 0 0 0 4 0 0
2 3 1 2 1 0 0 0 0 0 4 0
4 1 4 2 1 0 0 0 0 0 0 4
the automorphism group has order 1
and is strongly generated by the following 0 elements:
(
)
acting on the columns of the generator matrix as follows (in order):
orbits: { 1 }, { 2 }, { 3 }, { 4 }, { 5 }, { 6 }, { 7 }, { 8 }, { 9 }, { 10 }, { 11 }, { 12 }

code no      16:
================
1 1 1 1 1 4 0 0 0 0 0 0
2 2 1 1 0 0 4 0 0 0 0 0
3 1 2 1 0 0 0 4 0 0 0 0
3 2 1 0 1 0 0 0 4 0 0 0
4 4 3 1 1 0 0 0 0 4 0 0
3 4 4 2 1 0 0 0 0 0 4 0
1 2 0 3 1 0 0 0 0 0 0 4
the automorphism group has order 2
and is strongly generated by the following 1 elements:
(
2 4 0 1 2 
4 2 2 1 3 
0 0 0 0 1 
4 4 4 4 4 
0 0 4 0 0 
)
acting on the columns of the generator matrix as follows (in order):
(1, 12)(2, 11)(3, 5)(4, 6)
orbits: { 1, 12 }, { 2, 11 }, { 3, 5 }, { 4, 6 }, { 7 }, { 8 }, { 9 }, { 10 }

code no      17:
================
1 1 1 1 1 4 0 0 0 0 0 0
2 2 1 1 0 0 4 0 0 0 0 0
3 1 2 1 0 0 0 4 0 0 0 0
4 2 1 0 1 0 0 0 4 0 0 0
1 4 3 0 1 0 0 0 0 4 0 0
3 3 0 1 1 0 0 0 0 0 4 0
4 1 4 2 1 0 0 0 0 0 0 4
the automorphism group has order 1
and is strongly generated by the following 0 elements:
(
)
acting on the columns of the generator matrix as follows (in order):
orbits: { 1 }, { 2 }, { 3 }, { 4 }, { 5 }, { 6 }, { 7 }, { 8 }, { 9 }, { 10 }, { 11 }, { 12 }

code no      18:
================
1 1 1 1 1 4 0 0 0 0 0 0
2 2 1 1 0 0 4 0 0 0 0 0
3 1 2 1 0 0 0 4 0 0 0 0
4 2 1 0 1 0 0 0 4 0 0 0
1 4 3 0 1 0 0 0 0 4 0 0
3 2 3 1 1 0 0 0 0 0 4 0
0 1 2 3 1 0 0 0 0 0 0 4
the automorphism group has order 1
and is strongly generated by the following 0 elements:
(
)
acting on the columns of the generator matrix as follows (in order):
orbits: { 1 }, { 2 }, { 3 }, { 4 }, { 5 }, { 6 }, { 7 }, { 8 }, { 9 }, { 10 }, { 11 }, { 12 }

code no      19:
================
1 1 1 1 1 4 0 0 0 0 0 0
2 2 1 1 0 0 4 0 0 0 0 0
3 1 2 1 0 0 0 4 0 0 0 0
4 2 1 0 1 0 0 0 4 0 0 0
1 4 3 0 1 0 0 0 0 4 0 0
3 2 3 1 1 0 0 0 0 0 4 0
2 4 4 3 1 0 0 0 0 0 0 4
the automorphism group has order 1
and is strongly generated by the following 0 elements:
(
)
acting on the columns of the generator matrix as follows (in order):
orbits: { 1 }, { 2 }, { 3 }, { 4 }, { 5 }, { 6 }, { 7 }, { 8 }, { 9 }, { 10 }, { 11 }, { 12 }

code no      20:
================
1 1 1 1 1 4 0 0 0 0 0 0
2 2 1 1 0 0 4 0 0 0 0 0
3 1 2 1 0 0 0 4 0 0 0 0
4 2 1 0 1 0 0 0 4 0 0 0
3 2 0 1 1 0 0 0 0 4 0 0
4 3 4 2 1 0 0 0 0 0 4 0
3 1 4 3 1 0 0 0 0 0 0 4
the automorphism group has order 1
and is strongly generated by the following 0 elements:
(
)
acting on the columns of the generator matrix as follows (in order):
orbits: { 1 }, { 2 }, { 3 }, { 4 }, { 5 }, { 6 }, { 7 }, { 8 }, { 9 }, { 10 }, { 11 }, { 12 }

code no      21:
================
1 1 1 1 1 4 0 0 0 0 0 0
2 2 1 1 0 0 4 0 0 0 0 0
3 1 2 1 0 0 0 4 0 0 0 0
4 2 1 0 1 0 0 0 4 0 0 0
3 3 0 1 1 0 0 0 0 4 0 0
0 2 2 1 1 0 0 0 0 0 4 0
2 0 1 3 1 0 0 0 0 0 0 4
the automorphism group has order 1
and is strongly generated by the following 0 elements:
(
)
acting on the columns of the generator matrix as follows (in order):
orbits: { 1 }, { 2 }, { 3 }, { 4 }, { 5 }, { 6 }, { 7 }, { 8 }, { 9 }, { 10 }, { 11 }, { 12 }

code no      22:
================
1 1 1 1 1 4 0 0 0 0 0 0
2 2 1 1 0 0 4 0 0 0 0 0
3 1 2 1 0 0 0 4 0 0 0 0
4 2 1 0 1 0 0 0 4 0 0 0
3 3 0 1 1 0 0 0 0 4 0 0
4 3 4 2 1 0 0 0 0 0 4 0
3 2 4 3 1 0 0 0 0 0 0 4
the automorphism group has order 1
and is strongly generated by the following 0 elements:
(
)
acting on the columns of the generator matrix as follows (in order):
orbits: { 1 }, { 2 }, { 3 }, { 4 }, { 5 }, { 6 }, { 7 }, { 8 }, { 9 }, { 10 }, { 11 }, { 12 }

code no      23:
================
1 1 1 1 1 4 0 0 0 0 0 0
2 2 1 1 0 0 4 0 0 0 0 0
3 1 2 1 0 0 0 4 0 0 0 0
4 2 1 0 1 0 0 0 4 0 0 0
4 3 0 1 1 0 0 0 0 4 0 0
3 1 4 3 1 0 0 0 0 0 4 0
1 0 3 4 1 0 0 0 0 0 0 4
the automorphism group has order 1
and is strongly generated by the following 0 elements:
(
)
acting on the columns of the generator matrix as follows (in order):
orbits: { 1 }, { 2 }, { 3 }, { 4 }, { 5 }, { 6 }, { 7 }, { 8 }, { 9 }, { 10 }, { 11 }, { 12 }

code no      24:
================
1 1 1 1 1 4 0 0 0 0 0 0
2 2 1 1 0 0 4 0 0 0 0 0
3 1 2 1 0 0 0 4 0 0 0 0
4 2 1 0 1 0 0 0 4 0 0 0
0 2 2 1 1 0 0 0 0 4 0 0
3 0 3 1 1 0 0 0 0 0 4 0
2 0 1 3 1 0 0 0 0 0 0 4
the automorphism group has order 1
and is strongly generated by the following 0 elements:
(
)
acting on the columns of the generator matrix as follows (in order):
orbits: { 1 }, { 2 }, { 3 }, { 4 }, { 5 }, { 6 }, { 7 }, { 8 }, { 9 }, { 10 }, { 11 }, { 12 }

code no      25:
================
1 1 1 1 1 4 0 0 0 0 0 0
2 2 1 1 0 0 4 0 0 0 0 0
3 1 2 1 0 0 0 4 0 0 0 0
4 2 1 0 1 0 0 0 4 0 0 0
0 2 2 1 1 0 0 0 0 4 0 0
3 1 0 3 1 0 0 0 0 0 4 0
2 0 1 3 1 0 0 0 0 0 0 4
the automorphism group has order 2
and is strongly generated by the following 1 elements:
(
4 0 2 1 2 
0 2 0 0 0 
1 2 0 1 2 
0 3 3 4 4 
3 4 2 0 2 
)
acting on the columns of the generator matrix as follows (in order):
(1, 12)(3, 11)(4, 10)(5, 9)(6, 8)
orbits: { 1, 12 }, { 2 }, { 3, 11 }, { 4, 10 }, { 5, 9 }, { 6, 8 }, { 7 }

code no      26:
================
1 1 1 1 1 4 0 0 0 0 0 0
2 2 1 1 0 0 4 0 0 0 0 0
3 1 2 1 0 0 0 4 0 0 0 0
4 2 1 0 1 0 0 0 4 0 0 0
0 2 2 1 1 0 0 0 0 4 0 0
2 0 1 3 1 0 0 0 0 0 4 0
4 1 0 4 1 0 0 0 0 0 0 4
the automorphism group has order 1
and is strongly generated by the following 0 elements:
(
)
acting on the columns of the generator matrix as follows (in order):
orbits: { 1 }, { 2 }, { 3 }, { 4 }, { 5 }, { 6 }, { 7 }, { 8 }, { 9 }, { 10 }, { 11 }, { 12 }

code no      27:
================
1 1 1 1 1 4 0 0 0 0 0 0
2 2 1 1 0 0 4 0 0 0 0 0
3 1 2 1 0 0 0 4 0 0 0 0
4 2 1 0 1 0 0 0 4 0 0 0
3 0 3 1 1 0 0 0 0 4 0 0
4 3 4 2 1 0 0 0 0 0 4 0
3 1 4 3 1 0 0 0 0 0 0 4
the automorphism group has order 2
and is strongly generated by the following 1 elements:
(
3 3 4 4 0 
0 4 0 0 0 
3 1 2 1 0 
0 0 0 1 0 
1 2 1 3 4 
)
acting on the columns of the generator matrix as follows (in order):
(1, 7)(3, 8)(5, 11)(6, 10)
orbits: { 1, 7 }, { 2 }, { 3, 8 }, { 4 }, { 5, 11 }, { 6, 10 }, { 9 }, { 12 }

code no      28:
================
1 1 1 1 1 4 0 0 0 0 0 0
2 2 1 1 0 0 4 0 0 0 0 0
3 1 2 1 0 0 0 4 0 0 0 0
4 2 1 0 1 0 0 0 4 0 0 0
3 0 3 1 1 0 0 0 0 4 0 0
4 3 4 2 1 0 0 0 0 0 4 0
3 4 4 3 1 0 0 0 0 0 0 4
the automorphism group has order 4
and is strongly generated by the following 1 elements:
(
4 3 1 3 0 
0 2 0 0 0 
2 0 0 0 0 
0 0 0 4 0 
4 0 4 3 3 
)
acting on the columns of the generator matrix as follows (in order):
(1, 3, 7, 8)(5, 6, 11, 10)
orbits: { 1, 8, 7, 3 }, { 2 }, { 4 }, { 5, 10, 11, 6 }, { 9 }, { 12 }

code no      29:
================
1 1 1 1 1 4 0 0 0 0 0 0
2 2 1 1 0 0 4 0 0 0 0 0
3 1 2 1 0 0 0 4 0 0 0 0
4 2 1 0 1 0 0 0 4 0 0 0
3 0 3 1 1 0 0 0 0 4 0 0
4 3 4 2 1 0 0 0 0 0 4 0
1 3 0 4 1 0 0 0 0 0 0 4
the automorphism group has order 4
and is strongly generated by the following 1 elements:
(
4 3 1 3 0 
0 2 0 0 0 
2 0 0 0 0 
0 0 0 4 0 
4 0 4 3 3 
)
acting on the columns of the generator matrix as follows (in order):
(1, 3, 7, 8)(5, 6, 11, 10)
orbits: { 1, 8, 7, 3 }, { 2 }, { 4 }, { 5, 10, 11, 6 }, { 9 }, { 12 }

code no      30:
================
1 1 1 1 1 4 0 0 0 0 0 0
2 2 1 1 0 0 4 0 0 0 0 0
3 1 2 1 0 0 0 4 0 0 0 0
4 2 1 0 1 0 0 0 4 0 0 0
3 0 3 1 1 0 0 0 0 4 0 0
2 0 1 3 1 0 0 0 0 0 4 0
3 2 4 3 1 0 0 0 0 0 0 4
the automorphism group has order 1
and is strongly generated by the following 0 elements:
(
)
acting on the columns of the generator matrix as follows (in order):
orbits: { 1 }, { 2 }, { 3 }, { 4 }, { 5 }, { 6 }, { 7 }, { 8 }, { 9 }, { 10 }, { 11 }, { 12 }

code no      31:
================
1 1 1 1 1 4 0 0 0 0 0 0
2 2 1 1 0 0 4 0 0 0 0 0
3 1 2 1 0 0 0 4 0 0 0 0
4 2 1 0 1 0 0 0 4 0 0 0
0 2 4 1 1 0 0 0 0 4 0 0
4 1 0 2 1 0 0 0 0 0 4 0
3 4 4 3 1 0 0 0 0 0 0 4
the automorphism group has order 4
and is strongly generated by the following 1 elements:
(
0 4 0 0 0 
1 1 3 3 0 
0 0 4 0 0 
3 0 0 0 0 
3 2 0 4 2 
)
acting on the columns of the generator matrix as follows (in order):
(1, 4, 7, 2)(5, 9, 10, 11)
orbits: { 1, 2, 7, 4 }, { 3 }, { 5, 11, 10, 9 }, { 6 }, { 8 }, { 12 }

code no      32:
================
1 1 1 1 1 4 0 0 0 0 0 0
2 2 1 1 0 0 4 0 0 0 0 0
3 1 2 1 0 0 0 4 0 0 0 0
4 2 1 0 1 0 0 0 4 0 0 0
1 0 2 2 1 0 0 0 0 4 0 0
2 0 1 3 1 0 0 0 0 0 4 0
4 1 0 4 1 0 0 0 0 0 0 4
the automorphism group has order 1
and is strongly generated by the following 0 elements:
(
)
acting on the columns of the generator matrix as follows (in order):
orbits: { 1 }, { 2 }, { 3 }, { 4 }, { 5 }, { 6 }, { 7 }, { 8 }, { 9 }, { 10 }, { 11 }, { 12 }

code no      33:
================
1 1 1 1 1 4 0 0 0 0 0 0
2 2 1 1 0 0 4 0 0 0 0 0
3 1 2 1 0 0 0 4 0 0 0 0
2 3 1 0 1 0 0 0 4 0 0 0
3 4 2 0 1 0 0 0 0 4 0 0
0 2 2 1 1 0 0 0 0 0 4 0
3 0 3 1 1 0 0 0 0 0 0 4
the automorphism group has order 2
and is strongly generated by the following 1 elements:
(
0 4 0 0 0 
1 0 0 0 0 
0 0 3 0 0 
3 3 3 3 3 
1 3 4 0 2 
)
acting on the columns of the generator matrix as follows (in order):
(1, 2)(4, 6)(5, 10)(7, 11)(8, 12)
orbits: { 1, 2 }, { 3 }, { 4, 6 }, { 5, 10 }, { 7, 11 }, { 8, 12 }, { 9 }

code no      34:
================
1 1 1 1 1 4 0 0 0 0 0 0
2 2 1 1 0 0 4 0 0 0 0 0
3 1 2 1 0 0 0 4 0 0 0 0
2 3 1 0 1 0 0 0 4 0 0 0
2 4 2 1 1 0 0 0 0 4 0 0
0 1 2 2 1 0 0 0 0 0 4 0
1 4 0 3 1 0 0 0 0 0 0 4
the automorphism group has order 2
and is strongly generated by the following 1 elements:
(
0 0 0 0 4 
0 3 0 0 0 
0 0 3 0 0 
4 3 4 2 2 
1 0 0 0 0 
)
acting on the columns of the generator matrix as follows (in order):
(1, 5)(4, 10)(6, 11)(8, 12)
orbits: { 1, 5 }, { 2 }, { 3 }, { 4, 10 }, { 6, 11 }, { 7 }, { 8, 12 }, { 9 }

code no      35:
================
1 1 1 1 1 4 0 0 0 0 0 0
2 2 1 1 0 0 4 0 0 0 0 0
3 1 2 1 0 0 0 4 0 0 0 0
2 3 1 0 1 0 0 0 4 0 0 0
2 4 2 1 1 0 0 0 0 4 0 0
3 4 3 2 1 0 0 0 0 0 4 0
1 0 4 4 1 0 0 0 0 0 0 4
the automorphism group has order 4
and is strongly generated by the following 1 elements:
(
2 0 0 0 0 
1 2 4 2 0 
3 1 3 4 4 
1 0 4 4 1 
0 0 0 0 1 
)
acting on the columns of the generator matrix as follows (in order):
(2, 9, 6, 8)(3, 10)(4, 7, 11, 12)
orbits: { 1 }, { 2, 8, 6, 9 }, { 3, 10 }, { 4, 12, 11, 7 }, { 5 }

code no      36:
================
1 1 1 1 1 4 0 0 0 0 0 0
2 2 1 1 0 0 4 0 0 0 0 0
3 1 2 1 0 0 0 4 0 0 0 0
3 3 1 0 1 0 0 0 4 0 0 0
1 4 4 0 1 0 0 0 0 4 0 0
2 3 4 2 1 0 0 0 0 0 4 0
0 3 2 3 1 0 0 0 0 0 0 4
the automorphism group has order 20
and is strongly generated by the following 4 elements:
(
1 0 0 0 0 
0 1 0 0 0 
0 0 4 0 0 
3 3 1 0 1 
2 2 1 1 0 
, 
1 0 0 0 0 
2 3 3 0 2 
0 0 4 0 0 
1 1 1 1 1 
1 1 2 0 2 
, 
1 0 0 0 0 
0 1 4 1 2 
0 0 4 0 0 
0 0 0 0 3 
0 0 0 2 0 
, 
1 0 0 0 0 
1 1 2 0 2 
0 0 3 0 0 
1 4 2 1 3 
0 1 0 0 0 
)
acting on the columns of the generator matrix as follows (in order):
(4, 9)(5, 7)(8, 10)(11, 12), 
(2, 10)(4, 6)(5, 9)(8, 11), 
(2, 12)(4, 5)(6, 7)(10, 11), 
(2, 5, 10, 9)(4, 8, 6, 11)(7, 12)
orbits: { 1 }, { 2, 10, 12, 9, 8, 11, 5, 7, 4, 6 }, { 3 }