the 14 isometry classes of irreducible [14,4,8]_3 codes are:

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

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

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

code no       4:
================
1 1 1 1 1 1 1 1 1 1 2 0 0 0
2 2 2 1 1 1 1 0 0 0 0 2 0 0
2 1 0 2 2 1 0 1 1 0 0 0 2 0
2 1 0 1 0 2 2 1 0 1 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 
0 1 0 0 0 0 0 0 0 0 
0 0 1 0 0 0 0 0 0 0 
0 0 0 0 0 1 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 0 0 0 1 0 0 0 0 0 
0 0 0 0 0 0 0 1 0 0 
0 0 0 0 0 0 0 0 0 1 
0 0 0 0 0 0 0 0 1 0 
, 
1 0 0 0 0 0 0 0 0 0 
0 0 1 0 0 0 0 0 0 0 
0 1 0 0 0 0 0 0 0 0 
0 0 0 0 1 0 0 0 0 0 
0 0 0 1 0 0 0 0 0 0 
0 0 0 0 0 0 1 0 0 0 
0 0 0 0 0 1 0 0 0 0 
2 2 2 2 2 2 2 2 2 2 
0 0 0 0 0 0 0 0 0 1 
0 0 0 0 0 0 0 0 1 0 
)
acting on the columns of the generator matrix as follows (in order):
(4, 6)(5, 7)(9, 10)(13, 14), 
(2, 3)(4, 5)(6, 7)(8, 11)(9, 10)
orbits: { 1 }, { 2, 3 }, { 4, 6, 5, 7 }, { 8, 11 }, { 9, 10 }, { 12 }, { 13, 14 }

code no       5:
================
1 1 1 1 1 1 1 1 1 1 2 0 0 0
2 2 2 1 1 1 1 0 0 0 0 2 0 0
2 1 0 2 2 1 0 1 1 0 0 0 2 0
2 2 0 1 0 2 2 1 0 1 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 
2 1 0 2 2 1 0 1 1 0 
0 0 1 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 1 0 0 
0 0 0 0 0 0 0 0 1 0 
0 0 0 0 0 2 0 0 0 0 
1 1 1 2 2 2 2 0 0 0 
0 0 0 1 0 0 0 0 0 0 
0 0 0 0 1 0 0 0 0 0 
1 1 1 1 1 1 1 1 1 1 
)
acting on the columns of the generator matrix as follows (in order):
(2, 13)(4, 8)(5, 9)(7, 12)(10, 11)
orbits: { 1 }, { 2, 13 }, { 3 }, { 4, 8 }, { 5, 9 }, { 6 }, { 7, 12 }, { 10, 11 }, { 14 }

code no       6:
================
1 1 1 1 1 1 1 1 1 1 2 0 0 0
2 2 2 1 1 1 1 0 0 0 0 2 0 0
2 1 0 2 2 1 0 1 1 0 0 0 2 0
0 2 2 1 0 2 2 1 0 1 0 0 0 2
the automorphism group has order 48
and is strongly generated by the following 4 elements:
(
1 0 0 0 0 0 0 0 0 0 
0 2 0 0 0 0 0 0 0 0 
2 1 0 2 2 1 0 1 1 0 
1 1 1 1 1 1 1 1 1 1 
0 0 0 0 0 0 0 0 0 2 
2 2 2 1 1 1 1 0 0 0 
0 0 0 0 0 0 1 0 0 0 
0 0 0 0 0 0 0 1 0 0 
0 0 0 0 0 0 0 0 1 0 
0 0 0 0 2 0 0 0 0 0 
, 
2 0 0 0 0 0 0 0 0 0 
1 2 0 1 1 2 0 2 2 0 
0 1 0 0 0 0 0 0 0 0 
2 2 2 2 2 2 2 2 2 2 
0 0 0 0 0 0 0 0 0 1 
0 0 0 0 0 0 2 0 0 0 
1 1 1 2 2 2 2 0 0 0 
0 0 0 0 1 0 0 0 0 0 
0 0 0 1 0 0 0 0 0 0 
0 0 0 0 0 0 0 2 0 0 
, 
0 0 0 0 0 0 1 0 0 0 
0 0 0 0 0 0 0 0 0 1 
0 0 0 0 2 0 0 0 0 0 
0 2 2 1 0 2 2 1 0 1 
0 0 0 0 0 0 0 2 0 0 
0 0 0 0 0 2 0 0 0 0 
1 1 1 2 2 2 2 0 0 0 
0 0 2 0 0 0 0 0 0 0 
0 0 0 1 0 0 0 0 0 0 
1 2 0 1 1 2 0 2 2 0 
, 
0 0 0 0 0 0 0 0 2 0 
0 0 0 0 2 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 1 
1 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 2 0 0 
0 0 0 2 0 0 0 0 0 0 
2 2 2 2 2 2 2 2 2 2 
1 2 0 1 1 2 0 2 2 0 
0 0 0 0 0 1 0 0 0 0 
0 0 2 0 0 0 0 0 0 0 
)
acting on the columns of the generator matrix as follows (in order):
(3, 13)(4, 11)(5, 10)(6, 12), 
(2, 3, 13)(4, 9, 11)(5, 8, 10)(6, 12, 7), 
(1, 12, 7)(2, 13, 10)(3, 8, 5)(4, 9, 14), 
(1, 4, 6, 9)(2, 13, 8, 5)(3, 10)(7, 14, 12, 11)
orbits: { 1, 7, 9, 12, 11, 4, 6, 14 }, { 2, 13, 10, 5, 3, 8 }

code no       7:
================
1 1 1 1 1 1 1 1 1 1 2 0 0 0
2 2 2 1 1 1 1 0 0 0 0 2 0 0
2 1 0 2 2 1 0 1 1 0 0 0 2 0
2 1 1 1 0 2 0 2 0 1 0 0 0 2
the automorphism group has order 39
and is strongly generated by the following 3 elements:
(
2 0 0 0 0 0 0 0 0 0 
0 2 0 0 0 0 0 0 0 0 
0 0 0 1 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 2 0 
2 1 1 1 0 2 0 2 0 1 
1 2 0 1 1 2 0 2 2 0 
2 2 2 2 2 2 2 2 2 2 
0 0 0 0 2 0 0 0 0 0 
0 0 1 0 0 0 0 0 0 0 
0 0 0 0 0 2 0 0 0 0 
, 
1 0 0 0 0 0 0 0 0 0 
0 0 2 0 0 0 0 0 0 0 
1 2 0 1 1 2 0 2 2 0 
0 0 0 0 0 0 0 2 0 0 
0 0 0 0 0 0 0 0 2 0 
2 2 2 1 1 1 1 0 0 0 
0 0 0 0 0 1 0 0 0 0 
2 2 2 2 2 2 2 2 2 2 
0 0 0 0 0 0 0 0 0 1 
0 0 0 0 2 0 0 0 0 0 
, 
2 0 0 0 0 0 0 0 0 0 
1 2 2 2 0 1 0 1 0 2 
0 0 0 1 0 0 0 0 0 0 
2 2 2 2 2 2 2 2 2 2 
0 0 0 0 0 0 1 0 0 0 
0 0 0 0 0 0 0 0 2 0 
1 2 0 1 1 2 0 2 2 0 
0 0 0 0 0 1 0 0 0 0 
0 0 0 0 0 0 0 1 0 0 
0 0 0 0 0 0 0 0 0 2 
)
acting on the columns of the generator matrix as follows (in order):
(3, 9, 4)(5, 8, 14)(6, 10, 13)(7, 12, 11), 
(2, 13, 3)(4, 11, 8)(5, 10, 9)(6, 7, 12), 
(2, 12, 14)(3, 11, 4)(5, 13, 7)(6, 8, 9)
orbits: { 1 }, { 2, 3, 14, 4, 13, 8, 12, 9, 11, 10, 5, 6, 7 }

code no       8:
================
1 1 1 1 1 1 1 1 1 1 2 0 0 0
2 2 2 1 1 1 1 0 0 0 0 2 0 0
2 2 0 2 2 1 0 1 1 0 0 0 2 0
2 2 0 1 0 2 2 1 0 1 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 
0 1 0 0 0 0 0 0 0 0 
0 0 1 0 0 0 0 0 0 0 
0 0 0 0 0 1 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 0 0 0 1 0 0 0 0 0 
0 0 0 0 0 0 0 1 0 0 
0 0 0 0 0 0 0 0 0 1 
0 0 0 0 0 0 0 0 1 0 
, 
0 1 0 0 0 0 0 0 0 0 
1 0 0 0 0 0 0 0 0 0 
0 0 1 0 0 0 0 0 0 0 
0 0 0 1 0 0 0 0 0 0 
0 0 0 0 1 0 0 0 0 0 
0 0 0 0 0 1 0 0 0 0 
0 0 0 0 0 0 1 0 0 0 
0 0 0 0 0 0 0 1 0 0 
0 0 0 0 0 0 0 0 1 0 
0 0 0 0 0 0 0 0 0 1 
)
acting on the columns of the generator matrix as follows (in order):
(4, 6)(5, 7)(9, 10)(13, 14), 
(1, 2)
orbits: { 1, 2 }, { 3 }, { 4, 6 }, { 5, 7 }, { 8 }, { 9, 10 }, { 11 }, { 12 }, { 13, 14 }

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

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

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

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

code no      13:
================
1 1 1 1 1 1 1 0 0 0 2 0 0 0
2 2 1 1 1 0 0 1 1 0 0 2 0 0
2 1 2 1 0 1 0 1 0 1 0 0 2 0
2 1 1 2 0 0 1 0 1 1 0 0 0 2
the automorphism group has order 48
and is strongly generated by the following 6 elements:
(
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 0 0 0 
0 0 2 0 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 
0 0 0 0 0 2 0 0 0 0 
0 0 0 0 0 0 0 0 2 0 
0 0 0 0 0 0 0 2 0 0 
0 0 0 0 0 0 0 0 0 2 
, 
2 0 0 0 0 0 0 0 0 0 
0 0 2 0 0 0 0 0 0 0 
0 2 0 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 0 
0 0 0 0 2 0 0 0 0 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 0 0 0 0 0 2 0 
, 
1 0 0 0 0 0 0 0 0 0 
0 0 0 1 0 0 0 0 0 0 
0 1 0 0 0 0 0 0 0 0 
0 0 1 0 0 0 0 0 0 0 
0 0 0 0 0 0 1 0 0 0 
0 0 0 0 1 0 0 0 0 0 
0 0 0 0 0 1 0 0 0 0 
0 0 0 0 0 0 0 0 1 0 
0 0 0 0 0 0 0 0 0 1 
0 0 0 0 0 0 0 1 0 0 
, 
0 2 0 0 0 0 0 0 0 0 
2 0 0 0 0 0 0 0 0 0 
0 0 1 0 0 0 0 0 0 0 
0 0 0 1 0 0 0 0 0 0 
0 0 0 0 1 0 0 0 0 0 
0 0 0 0 0 0 0 1 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 0 0 0 1 0 0 0 
0 0 0 0 0 0 0 0 0 1 
, 
0 0 2 0 0 0 0 0 0 0 
0 1 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 0 0 0 
0 0 0 0 0 0 0 1 0 0 
0 0 0 0 0 1 0 0 0 0 
0 0 0 0 0 0 0 0 0 1 
0 0 0 0 1 0 0 0 0 0 
0 0 0 0 0 0 0 0 1 0 
0 0 0 0 0 0 1 0 0 0 
, 
2 1 2 1 0 1 0 1 0 1 
2 2 2 2 2 2 2 0 0 0 
1 1 2 2 2 0 0 2 2 0 
1 2 2 1 0 0 2 0 2 2 
0 0 0 0 0 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 0 0 0 0 0 2 0 0 
0 0 0 0 0 2 0 0 0 0 
)
acting on the columns of the generator matrix as follows (in order):
(3, 4)(6, 7)(8, 9)(13, 14), 
(2, 3)(5, 6)(9, 10)(12, 13), 
(2, 3, 4)(5, 6, 7)(8, 10, 9)(12, 13, 14), 
(1, 2)(6, 8)(7, 9)(11, 12), 
(1, 3)(5, 8)(7, 10)(11, 13), 
(1, 12, 3, 11, 2, 13)(4, 14)(5, 7, 6, 10, 8, 9)
orbits: { 1, 2, 3, 13, 4, 11, 12, 14 }, { 5, 6, 7, 8, 9, 10 }

code no      14:
================
1 1 1 1 1 1 1 0 0 0 2 0 0 0
2 2 1 1 1 0 0 1 1 0 0 2 0 0
2 1 2 1 0 1 0 1 0 1 0 0 2 0
1 2 2 0 1 0 1 0 1 1 0 0 0 2
the automorphism group has order 16
and is strongly generated by the following 4 elements:
(
1 0 0 0 0 0 0 0 0 0 
0 1 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 0 0 
0 0 0 2 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 2 0 
0 0 0 0 0 0 0 2 0 0 
0 0 0 0 0 0 2 0 0 0 
0 0 0 0 0 2 0 0 0 0 
0 0 0 0 0 0 0 0 0 2 
, 
2 0 0 0 0 0 0 0 0 0 
0 2 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 2 
2 1 1 0 2 0 2 0 2 2 
1 2 1 2 0 2 0 2 0 2 
0 0 0 0 0 0 0 0 1 0 
0 0 0 0 0 0 0 1 0 0 
0 0 0 0 0 0 1 0 0 0 
0 0 0 0 0 1 0 0 0 0 
0 0 2 0 0 0 0 0 0 0 
, 
0 1 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 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 0 2 0 0 
0 0 0 0 0 0 0 0 2 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 0 2 
, 
0 0 1 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 1 
0 1 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 1 0 
0 0 0 0 0 2 0 0 0 0 
2 1 1 0 2 0 2 0 2 2 
0 0 0 2 0 0 0 0 0 0 
0 0 0 0 1 0 0 0 0 0 
2 1 2 1 0 1 0 1 0 1 
1 0 0 0 0 0 0 0 0 0 
)
acting on the columns of the generator matrix as follows (in order):
(4, 5)(6, 9)(7, 8)(11, 12)(13, 14), 
(3, 10)(4, 14)(5, 13)(6, 9)(7, 8), 
(1, 2)(6, 8)(7, 9)(11, 12), 
(1, 10, 2, 3)(4, 7, 13, 9)(5, 8, 14, 6)
orbits: { 1, 2, 3, 10 }, { 4, 5, 14, 9, 13, 6, 8, 7 }, { 11, 12 }