the 6 isometry classes of irreducible [24,7,10]_2 codes are:

code no       1:
================
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0
1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
1 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 0 1 0 0 0 0
1 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 0 0 0 1 0 0 0
1 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 0 0 0 0 1 0 0
1 0 0 1 1 0 1 0 1 0 1 1 0 1 0 0 1 0 0 0 0 0 1 0
1 0 1 1 0 0 0 1 1 1 0 0 1 0 1 0 1 0 0 0 0 0 0 1
the automorphism group has order 12
and is strongly generated by the following 3 elements:
(
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 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 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 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 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 
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 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 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 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 0 0 0 0 0 0 0 0 
, 
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 
1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 
1 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 
0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 
0 0 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 0 0 1 0 0 0 0 
1 0 0 1 1 0 1 0 1 0 1 1 0 1 0 0 1 
1 1 1 1 1 0 0 0 0 1 1 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 0 0 0 0 0 0 1 0 0 0 
0 0 1 0 0 0 0 0 0 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 
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 0 0 0 0 0 0 1 0 0 
1 0 0 0 0 0 0 0 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 0 
, 
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 
1 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 
1 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 
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 0 0 
0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 
1 0 1 1 0 0 0 1 1 1 0 0 1 0 1 0 1 
1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 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 0 0 0 0 
0 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 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 0 
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 
0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 
)
acting on the columns of the generator matrix as follows (in order):
(1, 17)(2, 18)(3, 13)(4, 9)(6, 16)(7, 12)(10, 15)(19, 21)(20, 22), 
(1, 16)(2, 19)(3, 12)(4, 22)(6, 17)(7, 13)(8, 23)(9, 20)(11, 14)(18, 21), 
(1, 21, 4)(2, 6, 20)(3, 15, 12)(5, 11, 14)(7, 13, 10)(8, 23, 24)(9, 17, 19)(16, 22, 18)
orbits: { 1, 17, 16, 4, 6, 9, 18, 22, 21, 2, 20, 19 }, { 3, 13, 12, 7, 15, 10 }, { 5, 14, 11 }, { 8, 23, 24 }

code no       2:
================
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0
1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
1 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 0 1 0 0 0 0
1 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 0 0 0 1 0 0 0
1 0 0 1 1 1 0 1 0 1 0 1 0 1 0 1 0 0 0 0 0 1 0 0
1 1 0 1 0 0 0 1 1 0 1 0 1 0 1 1 0 0 0 0 0 0 1 0
1 0 1 0 0 1 0 1 1 0 1 1 0 1 0 0 1 0 0 0 0 0 0 1
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 0 0 0 0 0 0 0 
0 0 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 0 0 0 0 1 0 0 0 0 0 0 0 0 0 
1 0 0 1 1 1 0 1 0 1 0 1 0 1 0 1 0 
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 
0 0 1 0 0 0 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 0 0 0 
1 1 0 1 0 0 0 1 1 0 1 0 1 0 1 1 0 
1 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 
1 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 
0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 
1 0 1 0 0 1 0 1 1 0 1 1 0 1 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 0 0 0 0 0 0 0 0 0 0 0 0 
1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 
)
acting on the columns of the generator matrix as follows (in order):
(2, 16)(3, 7)(4, 8)(5, 22)(6, 18)(9, 23)(10, 20)(11, 15)(12, 21)(14, 24)(17, 19)
orbits: { 1 }, { 2, 16 }, { 3, 7 }, { 4, 8 }, { 5, 22 }, { 6, 18 }, { 9, 23 }, { 10, 20 }, { 11, 15 }, { 12, 21 }, { 13 }, { 14, 24 }, { 17, 19 }

code no       3:
================
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0
1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
1 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 0 1 0 0 0 0
1 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 0 0 0 1 0 0 0
1 0 0 1 1 1 0 1 0 1 0 1 0 1 0 1 0 0 0 0 0 1 0 0
1 1 0 1 0 1 0 0 1 0 0 0 1 1 1 1 0 0 0 0 0 0 1 0
0 1 0 1 0 1 1 1 0 0 1 1 0 1 0 0 1 0 0 0 0 0 0 1
the automorphism group has order 8
and is strongly generated by the following 3 elements:
(
1 0 0 0 0 0 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 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 0 0 0 0 0 0 0 
0 0 1 0 0 0 0 0 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 0 
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 0 0 0 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 0 0 0 0 0 0 0 1 0 0 0 0 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 0 0 0 0 0 1 0 0 0 0 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 0 0 0 0 0 0 0 1 0 0 0 
0 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 0 0 0 0 0 1 0 0 
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 
, 
1 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 
1 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 
0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 
1 0 0 1 1 1 0 1 0 1 0 1 0 1 0 1 0 
0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 
0 1 0 1 0 1 1 1 0 0 1 1 0 1 0 0 1 
0 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 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 0 0 0 0 0 0 1 0 0 0 0 
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 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 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 0 0 0 0 0 1 0 0 0 0 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 0 0 1 0 0 0 0 0 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 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 
0 0 0 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 0 0 1 0 0 0 0 0 0 0 0 0 0 
1 1 0 1 0 1 0 0 1 0 0 0 1 1 1 1 0 
1 0 0 0 0 0 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 0 0 0 
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
1 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 
0 1 0 1 0 1 1 1 0 0 1 1 0 1 0 0 1 
1 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 
1 0 0 1 1 1 0 1 0 1 0 1 0 1 0 1 0 
0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 
)
acting on the columns of the generator matrix as follows (in order):
(2, 4)(3, 5)(7, 8)(11, 12)(15, 16)(21, 22), 
(1, 20)(2, 21)(3, 8)(4, 22)(5, 7)(6, 24)(10, 13)(11, 15)(12, 16)(14, 17)(18, 19), 
(1, 10)(2, 12)(4, 11)(6, 17)(7, 8)(9, 23)(13, 20)(14, 24)(15, 21)(16, 22)(18, 19)
orbits: { 1, 20, 10, 13 }, { 2, 4, 21, 12, 22, 11, 15, 16 }, { 3, 5, 8, 7 }, { 6, 24, 17, 14 }, { 9, 23 }, { 18, 19 }

code no       4:
================
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0
1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
1 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 0 1 0 0 0 0
1 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 0 0 0 1 0 0 0
1 0 0 1 1 1 0 1 0 1 0 1 0 1 0 1 0 0 0 0 0 1 0 0
0 1 0 1 0 1 1 1 0 0 1 1 0 1 0 0 1 0 0 0 0 0 1 0
1 1 0 1 0 1 0 0 1 0 0 0 1 0 1 1 1 0 0 0 0 0 0 1
the automorphism group has order 384
and is strongly generated by the following 7 elements:
(
1 0 0 0 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 0 0 0 0 0 
0 0 1 0 0 0 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 0 0 0 
0 0 0 0 1 0 0 0 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 0 
0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 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 0 0 0 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 0 0 0 0 0 0 0 1 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 
1 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 
1 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 
1 0 0 1 1 1 0 1 0 1 0 1 0 1 0 1 0 
0 1 0 1 0 1 1 1 0 0 1 1 0 1 0 0 1 
, 
1 0 0 0 0 0 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 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 0 0 0 0 0 0 0 
0 0 1 0 0 0 0 0 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 0 
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 0 0 0 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 0 0 0 0 0 0 0 1 0 0 0 0 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 0 0 0 0 0 1 0 0 0 0 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 0 0 0 0 0 0 0 1 0 0 0 
0 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 0 0 0 0 0 1 0 0 
0 0 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 
1 1 0 1 0 1 0 0 1 0 0 0 1 0 1 1 1 
0 1 0 1 0 1 1 1 0 0 1 1 0 1 0 0 1 
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 
0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 
1 1 1 1 1 0 0 0 0 1 1 1 1 0 0 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 0 0 0 0 1 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 
1 1 1 1 1 1 1 1 1 0 0 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 0 0 0 0 1 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 1 0 
1 0 0 1 1 1 0 1 0 1 0 1 0 1 0 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 0 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 0 0 0 0 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 0 0 
0 0 0 1 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 1 0 0 0 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 0 0 0 0 0 0 0 1 0 0 0 0 
0 0 0 0 0 1 0 0 0 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 
0 0 0 0 0 0 0 1 0 0 0 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 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 0 0 0 1 0 0 
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 
, 
1 0 0 1 1 1 0 1 0 1 0 1 0 1 0 1 0 
0 1 0 1 0 1 1 1 0 0 1 1 0 1 0 0 1 
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
1 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 
0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 
1 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 
0 0 0 0 1 0 0 0 0 0 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 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 
0 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 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 0 0 0 0 1 0 0 0 0 0 
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 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 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 
0 0 0 0 0 1 0 0 0 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 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 
0 0 0 1 0 0 0 0 0 0 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 0 0 0 1 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 1 0 0 0 0 0 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 0 0 1 0 0 0 0 0 0 0 
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 0 0 0 1 0 0 0 0 0 
0 0 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 0 0 1 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 
, 
1 1 0 1 0 1 0 0 1 0 0 0 1 0 1 1 1 
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 
1 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
1 0 0 1 1 1 0 1 0 1 0 1 0 1 0 1 0 
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 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 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 1 1 1 1 1 1 1 1 0 0 0 0 0 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 0 0 0 0 0 1 0 0 0 0 0 0 
0 0 0 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 
0 0 1 0 0 0 0 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 0 0 
0 1 0 1 0 1 1 1 0 0 1 1 0 1 0 0 1 
)
acting on the columns of the generator matrix as follows (in order):
(9, 19)(13, 20)(15, 21)(16, 22)(17, 23)(18, 24), 
(2, 4)(3, 5)(7, 8)(11, 12)(15, 16)(21, 22), 
(2, 18, 4, 24)(3, 17, 5, 23)(7, 13, 8, 20)(9, 12, 19, 11)(15, 21, 22, 16), 
(2, 3)(4, 5)(6, 10)(7, 11)(8, 12)(9, 13)(17, 18)(19, 20)(23, 24), 
(1, 22)(2, 23)(4, 20)(5, 7)(6, 21)(10, 16)(11, 17)(12, 13)(14, 15)(18, 19), 
(1, 4, 6, 2)(3, 5, 8, 7)(10, 12, 14, 11)(13, 16, 17, 15)(20, 22, 23, 21), 
(1, 18, 6, 24)(2, 4)(3, 15, 7, 21)(5, 16, 8, 22)(9, 14, 19, 10)(11, 12)(13, 20, 23, 17)
orbits: { 1, 22, 2, 24, 16, 21, 20, 8, 4, 3, 23, 6, 18, 15, 10, 13, 5, 7, 19, 12, 17, 14, 11, 9 }

code no       5:
================
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0
1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
1 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 0 1 0 0 0 0
1 1 0 0 0 1 1 1 0 1 1 0 0 1 1 0 0 0 0 0 1 0 0 0
0 0 1 1 0 1 1 0 1 1 0 1 0 1 0 1 0 0 0 0 0 1 0 0
1 0 1 0 0 1 0 0 1 1 1 0 1 0 1 1 0 0 0 0 0 0 1 0
0 0 1 0 1 1 0 1 0 1 1 1 0 1 0 0 1 0 0 0 0 0 0 1
the automorphism group has order 48
and is strongly generated by the following 3 elements:
(
1 0 0 0 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 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 0 0 0 1 0 0 0 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 0 1 0 0 0 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 0 0 0 
0 0 0 0 1 0 0 0 0 0 0 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 0 0 0 0 0 0 0 1 0 0 0 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 0 0 0 0 0 0 0 0 0 1 0 0 0 
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 0 0 0 1 0 0 0 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 0 0 0 0 0 0 0 0 0 1 0 
0 0 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 
1 0 1 0 0 1 0 0 1 1 1 0 1 0 1 1 0 
0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 
1 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 
0 0 1 0 0 0 0 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 0 0 
1 1 0 0 0 1 1 1 0 1 1 0 0 1 1 0 0 
0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 
0 0 1 1 0 1 1 0 1 1 0 1 0 1 0 1 0 
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 
1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 
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 0 0 0 1 0 0 0 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 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 
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 
, 
0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 
0 0 1 1 0 1 1 0 1 1 0 1 0 1 0 1 0 
0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 
0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 
1 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 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 0 0 0 0 
1 1 0 0 0 1 1 1 0 1 1 0 0 1 1 0 0 
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 
0 0 1 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 
1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 
1 0 1 0 0 1 0 0 1 1 1 0 1 0 1 1 0 
)
acting on the columns of the generator matrix as follows (in order):
(3, 6)(4, 7)(5, 8)(12, 14)(13, 15)(20, 21), 
(2, 23)(3, 5, 6, 8)(4, 21, 7, 20)(9, 22)(10, 16)(11, 19)(12, 13, 14, 15)(17, 18), 
(1, 18, 10)(2, 24, 22)(3, 12, 13, 6, 14, 15)(4, 20, 5, 7, 21, 8)(9, 19, 16)(11, 23, 17)
orbits: { 1, 10, 16, 18, 19, 17, 11, 9, 23, 22, 2, 24 }, { 3, 6, 8, 15, 5, 13, 21, 14, 20, 12, 4, 7 }

code no       6:
================
1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
1 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 1 0 0 0 0 0
1 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 0 0 1 0 0 0 0
1 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 0 0 0 1 0 0 0
1 1 0 0 1 0 1 1 0 0 1 1 0 1 0 0 1 0 0 0 0 1 0 0
1 0 1 0 1 1 0 0 1 0 0 0 1 0 1 1 1 0 0 0 0 0 1 0
1 0 0 1 0 0 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 1
the automorphism group has order 240
and is strongly generated by the following 4 elements:
(
1 0 0 0 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 0 0 0 0 0 
0 0 1 0 0 0 0 0 0 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 
0 0 0 0 0 1 0 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 0 0 
0 0 0 1 0 0 0 0 0 0 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 0 0 0 0 0 0 0 1 0 0 0 0 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 0 0 0 0 0 1 0 0 0 0 0 0 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 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 0 0 0 0 0 0 0 0 0 1 0 0 0 0 
0 0 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 0 0 0 0 0 1 0 
, 
1 0 0 0 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 0 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 0 0 0 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 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 0 0 0 0 1 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 
1 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 
0 0 0 0 0 1 0 0 0 0 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 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 
1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 
1 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 
1 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 
0 0 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 
0 1 0 0 0 0 0 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 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 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 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 1 
0 0 1 0 0 0 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 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 0 0 0 0 0 1 0 0 0 0 
0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 
1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 
1 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 
0 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 0 0 0 0 0 0 1 0 
1 1 0 1 0 1 0 1 0 1 0 1 0 1 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 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 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 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 0 0 0 0 0 0 
0 0 1 0 0 0 0 0 0 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 
0 0 0 0 1 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 
1 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 
0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 
1 1 0 0 1 0 1 1 0 0 1 1 0 1 0 0 1 
)
acting on the columns of the generator matrix as follows (in order):
(4, 7)(5, 6)(10, 11)(12, 14)(13, 15)(16, 17)(19, 20)(21, 22), 
(3, 4)(6, 10)(7, 12)(8, 11)(9, 19)(13, 18)(15, 21)(16, 20), 
(3, 10, 12, 5)(4, 11)(6, 14, 8, 7)(9, 20, 16, 17)(15, 21, 22, 18)(23, 24), 
(1, 9, 13, 16)(2, 18, 19, 21)(3, 10, 5, 12)(4, 7, 11, 14)(6, 8)(15, 20)(17, 22)
orbits: { 1, 16, 17, 20, 13, 22, 19, 9, 15, 18, 21, 2 }, { 3, 4, 5, 12, 7, 11, 14, 6, 10, 8 }, { 23, 24 }