the 22 isometry classes of irreducible [15,6,7]_3 codes are:

code no       1:
================
1 1 1 1 1 1 1 1 1 2 0 0 0 0 0
2 2 1 1 1 1 0 0 0 0 2 0 0 0 0
2 1 2 1 0 0 1 1 0 0 0 2 0 0 0
1 1 0 0 2 1 2 1 0 0 0 0 2 0 0
1 2 0 2 1 0 1 0 1 0 0 0 0 2 0
2 0 1 2 1 2 2 0 1 0 0 0 0 0 2
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 }, { 13 }, { 14 }, { 15 }

code no       2:
================
1 1 1 1 1 1 1 1 1 2 0 0 0 0 0
2 2 1 1 1 1 0 0 0 0 2 0 0 0 0
2 1 2 1 0 0 1 1 0 0 0 2 0 0 0
1 1 0 0 2 1 2 1 0 0 0 0 2 0 0
1 2 0 2 1 0 1 0 1 0 0 0 0 2 0
2 0 1 2 1 2 2 1 1 0 0 0 0 0 2
the automorphism group has order 2
and is strongly generated by the following 1 elements:
(
2 0 0 0 0 0 0 0 0 
0 0 0 0 2 0 0 0 0 
0 0 0 0 0 0 0 0 1 
0 0 0 2 0 0 0 0 0 
0 2 0 0 0 0 0 0 0 
2 1 0 1 2 0 2 0 2 
1 1 2 2 2 2 0 0 0 
2 0 1 2 1 2 2 1 1 
0 0 1 0 0 0 0 0 0 
)
acting on the columns of the generator matrix as follows (in order):
(2, 5)(3, 9)(6, 14)(7, 11)(8, 15)(12, 13)
orbits: { 1 }, { 2, 5 }, { 3, 9 }, { 4 }, { 6, 14 }, { 7, 11 }, { 8, 15 }, { 10 }, { 12, 13 }

code no       3:
================
1 1 1 1 1 1 1 1 1 2 0 0 0 0 0
2 2 1 1 1 1 0 0 0 0 2 0 0 0 0
2 1 2 1 0 0 1 1 0 0 0 2 0 0 0
1 1 0 0 2 1 2 1 0 0 0 0 2 0 0
1 2 0 2 2 0 1 0 1 0 0 0 0 2 0
2 0 1 2 0 2 2 0 1 0 0 0 0 0 2
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 }, { 13 }, { 14 }, { 15 }

code no       4:
================
1 1 1 1 1 1 1 1 1 2 0 0 0 0 0
2 2 1 1 1 1 0 0 0 0 2 0 0 0 0
2 1 2 1 0 0 1 1 0 0 0 2 0 0 0
1 1 0 0 2 1 2 1 0 0 0 0 2 0 0
1 2 0 2 2 0 1 0 1 0 0 0 0 2 0
2 0 0 1 0 1 1 2 1 0 0 0 0 0 2
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 }, { 13 }, { 14 }, { 15 }

code no       5:
================
1 1 1 1 1 1 1 1 1 2 0 0 0 0 0
2 2 1 1 1 1 0 0 0 0 2 0 0 0 0
2 1 2 1 0 0 1 1 0 0 0 2 0 0 0
1 1 0 0 2 1 2 1 0 0 0 0 2 0 0
2 1 0 2 0 1 1 0 1 0 0 0 0 2 0
1 2 1 0 2 0 0 1 1 0 0 0 0 0 2
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 }, { 13 }, { 14 }, { 15 }

code no       6:
================
1 1 1 1 1 1 1 1 1 2 0 0 0 0 0
2 2 1 1 1 1 0 0 0 0 2 0 0 0 0
2 1 2 1 0 0 1 1 0 0 0 2 0 0 0
1 1 0 0 2 1 2 1 0 0 0 0 2 0 0
0 2 1 2 0 2 1 0 1 0 0 0 0 2 0
2 0 2 1 2 1 2 1 1 0 0 0 0 0 2
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 }, { 13 }, { 14 }, { 15 }

code no       7:
================
1 1 1 1 1 1 1 1 1 2 0 0 0 0 0
2 2 1 1 1 1 0 0 0 0 2 0 0 0 0
2 1 2 1 0 0 1 1 0 0 0 2 0 0 0
1 1 0 0 2 1 2 1 0 0 0 0 2 0 0
0 2 1 2 0 2 1 0 1 0 0 0 0 2 0
0 2 2 1 1 0 1 2 1 0 0 0 0 0 2
the automorphism group has order 2
and is strongly generated by the following 1 elements:
(
0 2 0 0 0 0 0 0 0 
2 0 0 0 0 0 0 0 0 
0 0 2 0 0 0 0 0 0 
0 0 0 0 0 2 0 0 0 
2 2 1 1 1 1 0 0 0 
0 0 0 2 0 0 0 0 0 
0 1 1 2 2 0 2 1 2 
0 0 0 0 0 0 0 1 0 
0 0 0 0 0 0 0 0 1 
)
acting on the columns of the generator matrix as follows (in order):
(1, 2)(4, 6)(5, 11)(7, 15)(10, 12)(13, 14)
orbits: { 1, 2 }, { 3 }, { 4, 6 }, { 5, 11 }, { 7, 15 }, { 8 }, { 9 }, { 10, 12 }, { 13, 14 }

code no       8:
================
1 1 1 1 1 1 1 1 1 2 0 0 0 0 0
2 2 1 1 1 1 0 0 0 0 2 0 0 0 0
2 1 2 1 0 0 1 1 0 0 0 2 0 0 0
1 1 0 0 2 1 2 1 0 0 0 0 2 0 0
1 2 2 0 1 0 2 0 1 0 0 0 0 2 0
0 2 0 1 2 0 1 2 1 0 0 0 0 0 2
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 }, { 13 }, { 14 }, { 15 }

code no       9:
================
1 1 1 1 1 1 1 1 1 2 0 0 0 0 0
2 2 1 1 1 1 0 0 0 0 2 0 0 0 0
2 1 2 1 0 0 1 1 0 0 0 2 0 0 0
1 1 0 0 2 1 2 1 0 0 0 0 2 0 0
2 1 1 2 0 2 2 0 1 0 0 0 0 2 0
0 1 0 1 1 2 0 2 1 0 0 0 0 0 2
the automorphism group has order 2
and is strongly generated by the following 1 elements:
(
0 2 0 2 2 1 0 1 2 
1 2 2 1 0 1 1 0 2 
0 0 0 0 0 0 0 1 0 
1 1 2 2 2 2 0 0 0 
0 0 0 0 0 0 0 0 1 
0 0 0 0 0 0 1 0 0 
0 0 0 0 0 1 0 0 0 
0 0 1 0 0 0 0 0 0 
0 0 0 0 1 0 0 0 0 
)
acting on the columns of the generator matrix as follows (in order):
(1, 15)(2, 14)(3, 8)(4, 11)(5, 9)(6, 7)
orbits: { 1, 15 }, { 2, 14 }, { 3, 8 }, { 4, 11 }, { 5, 9 }, { 6, 7 }, { 10 }, { 12 }, { 13 }

code no      10:
================
1 1 1 1 1 1 1 1 1 2 0 0 0 0 0
2 2 1 1 1 1 0 0 0 0 2 0 0 0 0
2 1 2 1 0 0 1 1 0 0 0 2 0 0 0
2 1 0 0 2 1 2 1 0 0 0 0 2 0 0
0 2 2 1 1 0 1 0 1 0 0 0 0 2 0
2 0 1 0 2 1 1 2 1 0 0 0 0 0 2
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 }, { 13 }, { 14 }, { 15 }

code no      11:
================
1 1 1 1 1 1 1 1 1 2 0 0 0 0 0
2 2 1 1 1 1 0 0 0 0 2 0 0 0 0
2 1 2 1 0 0 1 1 0 0 0 2 0 0 0
2 1 0 0 2 1 2 1 0 0 0 0 2 0 0
2 1 0 2 1 0 1 0 1 0 0 0 0 2 0
0 0 2 1 0 1 2 1 1 0 0 0 0 0 2
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 }, { 13 }, { 14 }, { 15 }

code no      12:
================
1 1 1 1 1 1 1 1 1 2 0 0 0 0 0
2 2 1 1 1 1 0 0 0 0 2 0 0 0 0
2 1 2 1 0 0 1 1 0 0 0 2 0 0 0
2 1 0 0 2 1 2 1 0 0 0 0 2 0 0
0 2 1 2 1 0 1 0 1 0 0 0 0 2 0
2 1 0 2 2 0 1 2 1 0 0 0 0 0 2
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 }, { 13 }, { 14 }, { 15 }

code no      13:
================
1 1 1 1 1 1 1 1 1 2 0 0 0 0 0
2 2 1 1 1 1 0 0 0 0 2 0 0 0 0
2 1 2 1 0 0 1 1 0 0 0 2 0 0 0
2 1 0 0 2 1 2 1 0 0 0 0 2 0 0
0 2 2 1 0 1 1 0 1 0 0 0 0 2 0
0 0 1 0 1 2 2 1 1 0 0 0 0 0 2
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 }, { 13 }, { 14 }, { 15 }

code no      14:
================
1 1 1 1 1 1 1 1 1 2 0 0 0 0 0
2 2 1 1 1 1 0 0 0 0 2 0 0 0 0
2 1 2 1 0 0 1 1 0 0 0 2 0 0 0
2 1 0 0 2 1 2 1 0 0 0 0 2 0 0
1 2 2 0 2 1 1 0 1 0 0 0 0 2 0
0 1 1 2 0 2 2 1 1 0 0 0 0 0 2
the automorphism group has order 2
and is strongly generated by the following 1 elements:
(
2 1 2 1 0 0 1 1 0 
0 1 0 0 0 0 0 0 0 
0 0 2 0 0 0 0 0 0 
1 1 2 2 2 2 0 0 0 
1 1 1 1 1 1 1 1 1 
0 0 0 0 0 0 0 0 2 
2 1 1 0 1 2 2 0 2 
0 1 1 2 0 2 2 1 1 
0 0 0 0 0 2 0 0 0 
)
acting on the columns of the generator matrix as follows (in order):
(1, 12)(4, 11)(5, 10)(6, 9)(7, 14)(8, 15)
orbits: { 1, 12 }, { 2 }, { 3 }, { 4, 11 }, { 5, 10 }, { 6, 9 }, { 7, 14 }, { 8, 15 }, { 13 }

code no      15:
================
1 1 1 1 1 1 1 1 1 2 0 0 0 0 0
2 2 1 1 1 1 0 0 0 0 2 0 0 0 0
2 1 2 1 0 0 1 1 0 0 0 2 0 0 0
2 1 0 0 2 1 2 1 0 0 0 0 2 0 0
1 2 2 0 2 1 1 0 1 0 0 0 0 2 0
2 2 1 0 2 0 0 2 1 0 0 0 0 0 2
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 }, { 13 }, { 14 }, { 15 }

code no      16:
================
1 1 1 1 1 1 1 1 1 2 0 0 0 0 0
2 2 1 1 1 1 0 0 0 0 2 0 0 0 0
2 1 2 1 0 0 1 1 0 0 0 2 0 0 0
2 1 0 0 2 1 2 1 0 0 0 0 2 0 0
1 2 0 2 2 1 1 0 1 0 0 0 0 2 0
0 2 0 1 2 0 2 1 1 0 0 0 0 0 2
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 }, { 13 }, { 14 }, { 15 }

code no      17:
================
1 1 1 1 1 1 1 1 1 2 0 0 0 0 0
2 2 1 1 1 1 0 0 0 0 2 0 0 0 0
2 1 2 1 0 0 1 1 0 0 0 2 0 0 0
2 1 0 0 2 1 2 1 0 0 0 0 2 0 0
2 1 0 2 1 0 2 0 1 0 0 0 0 2 0
2 2 1 0 1 2 2 1 1 0 0 0 0 0 2
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 }, { 13 }, { 14 }, { 15 }

code no      18:
================
1 1 1 1 1 1 1 1 1 2 0 0 0 0 0
2 2 1 1 1 1 0 0 0 0 2 0 0 0 0
2 1 2 1 0 0 1 1 0 0 0 2 0 0 0
0 2 0 1 2 1 2 1 0 0 0 0 2 0 0
0 2 2 0 2 1 1 0 1 0 0 0 0 2 0
1 0 0 1 2 0 1 2 1 0 0 0 0 0 2
the automorphism group has order 2
and is strongly generated by the following 1 elements:
(
1 0 0 0 0 0 0 0 0 
0 2 0 1 2 1 2 1 0 
2 2 1 1 1 1 0 0 0 
0 0 0 1 0 0 0 0 0 
2 0 0 2 1 0 2 1 2 
0 0 0 0 0 0 0 0 1 
1 1 1 1 1 1 1 1 1 
0 1 1 0 1 2 2 0 2 
0 0 0 0 0 1 0 0 0 
)
acting on the columns of the generator matrix as follows (in order):
(2, 13)(3, 11)(5, 15)(6, 9)(7, 10)(8, 14)
orbits: { 1 }, { 2, 13 }, { 3, 11 }, { 4 }, { 5, 15 }, { 6, 9 }, { 7, 10 }, { 8, 14 }, { 12 }

code no      19:
================
1 1 1 1 1 1 1 1 1 2 0 0 0 0 0
2 2 1 1 1 1 0 0 0 0 2 0 0 0 0
2 1 2 1 0 0 1 1 0 0 0 2 0 0 0
0 2 0 1 2 1 2 1 0 0 0 0 2 0 0
1 2 2 0 0 2 1 0 1 0 0 0 0 2 0
2 1 0 0 1 2 2 1 1 0 0 0 0 0 2
the automorphism group has order 2
and is strongly generated by the following 1 elements:
(
0 0 0 0 0 0 0 2 0 
0 1 0 0 0 0 0 0 0 
0 1 0 2 1 2 1 2 0 
0 0 0 0 0 1 0 0 0 
0 0 0 0 2 0 0 0 0 
0 0 0 1 0 0 0 0 0 
2 2 1 1 1 1 0 0 0 
2 0 0 0 0 0 0 0 0 
2 2 2 2 2 2 2 2 2 
)
acting on the columns of the generator matrix as follows (in order):
(1, 8)(3, 13)(4, 6)(7, 11)(9, 10)(14, 15)
orbits: { 1, 8 }, { 2 }, { 3, 13 }, { 4, 6 }, { 5 }, { 7, 11 }, { 9, 10 }, { 12 }, { 14, 15 }

code no      20:
================
1 1 1 1 1 1 1 1 1 2 0 0 0 0 0
2 2 1 1 1 1 0 0 0 0 2 0 0 0 0
2 1 2 1 0 0 1 1 0 0 0 2 0 0 0
0 2 0 1 2 1 2 1 0 0 0 0 2 0 0
1 2 2 0 0 2 1 0 1 0 0 0 0 2 0
2 0 0 1 0 1 1 2 1 0 0 0 0 0 2
the automorphism group has order 4
and is strongly generated by the following 2 elements:
(
1 0 0 0 0 0 0 0 0 
0 2 0 0 0 0 0 0 0 
0 0 1 0 0 0 0 0 0 
2 0 0 1 0 1 1 2 1 
0 0 0 0 1 0 0 0 0 
2 2 2 2 2 2 2 2 2 
0 2 0 1 2 1 2 1 0 
2 2 1 1 1 1 0 0 0 
2 1 2 1 0 0 1 1 0 
, 
0 0 2 0 0 0 0 0 0 
0 2 0 0 0 0 0 0 0 
2 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 2 0 0 
1 2 2 0 0 2 1 0 1 
0 0 0 0 0 1 0 0 0 
0 0 0 2 0 0 0 0 0 
2 1 2 1 0 0 1 1 0 
2 2 1 1 1 1 0 0 0 
)
acting on the columns of the generator matrix as follows (in order):
(4, 15)(6, 10)(7, 13)(8, 11)(9, 12), 
(1, 3)(4, 7)(5, 14)(8, 12)(9, 11)(13, 15)
orbits: { 1, 3 }, { 2 }, { 4, 15, 7, 13 }, { 5, 14 }, { 6, 10 }, { 8, 11, 12, 9 }

code no      21:
================
1 1 1 1 1 1 1 1 1 2 0 0 0 0 0
2 2 1 1 1 1 0 0 0 0 2 0 0 0 0
2 1 2 1 0 0 1 1 0 0 0 2 0 0 0
0 2 2 1 2 1 2 1 0 0 0 0 2 0 0
0 2 2 2 0 1 1 0 1 0 0 0 0 2 0
0 2 0 1 1 2 0 1 1 0 0 0 0 0 2
the automorphism group has order 2
and is strongly generated by the following 1 elements:
(
0 2 2 2 0 1 1 0 1 
0 1 0 0 0 0 0 0 0 
0 1 1 2 1 2 1 2 0 
2 1 2 1 0 0 1 1 0 
0 0 0 0 0 0 0 0 1 
0 0 0 0 0 0 2 0 0 
0 0 0 0 0 2 0 0 0 
1 1 1 1 1 1 1 1 1 
0 0 0 0 1 0 0 0 0 
)
acting on the columns of the generator matrix as follows (in order):
(1, 14)(3, 13)(4, 12)(5, 9)(6, 7)(8, 10)
orbits: { 1, 14 }, { 2 }, { 3, 13 }, { 4, 12 }, { 5, 9 }, { 6, 7 }, { 8, 10 }, { 11 }, { 15 }

code no      22:
================
1 1 1 1 1 1 1 1 1 2 0 0 0 0 0
2 2 1 1 1 1 0 0 0 0 2 0 0 0 0
2 1 2 1 0 0 1 1 0 0 0 2 0 0 0
2 1 0 2 1 0 1 0 1 0 0 0 2 0 0
2 0 1 0 2 0 2 1 1 0 0 0 0 2 0
0 1 1 1 0 2 2 2 1 0 0 0 0 0 2
the automorphism group has order 3
and is strongly generated by the following 1 elements:
(
0 1 1 1 0 2 2 2 1 
1 1 1 1 1 1 1 1 1 
1 0 2 0 1 0 1 2 2 
0 0 0 0 0 0 2 0 0 
0 0 0 0 0 0 0 1 0 
0 0 0 2 0 0 0 0 0 
0 0 0 0 0 1 0 0 0 
0 0 0 0 0 0 0 0 2 
0 0 0 0 2 0 0 0 0 
)
acting on the columns of the generator matrix as follows (in order):
(1, 13, 15)(2, 11, 10)(3, 12, 14)(4, 6, 7)(5, 9, 8)
orbits: { 1, 15, 13 }, { 2, 10, 11 }, { 3, 14, 12 }, { 4, 7, 6 }, { 5, 8, 9 }