the 8 isometry classes of irreducible [24,18,4]_2 codes are:

code no       1:
================
1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 0 1 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 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
1 0 1 0 1 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 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
1 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
0 1 0 1 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 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
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 1 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 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
the automorphism group has order 516096
and is strongly generated by the following 13 elements:
(
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
0 0 0 1 0 0 
0 0 0 0 1 0 
1 1 0 0 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
0 0 0 1 0 0 
0 0 0 0 1 0 
1 0 1 0 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
0 0 0 1 0 0 
0 0 0 0 1 0 
1 0 0 1 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
0 0 0 1 0 0 
0 0 1 1 1 0 
0 0 0 0 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
0 0 0 1 0 0 
0 1 0 1 1 0 
0 0 0 0 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
0 0 0 1 0 0 
1 0 0 1 1 0 
0 0 0 0 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
0 0 0 1 0 0 
0 0 1 1 0 1 
0 0 1 1 1 0 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
1 1 0 1 0 0 
1 0 1 0 1 0 
1 1 0 0 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
1 0 1 1 0 0 
1 1 0 0 1 0 
1 0 1 0 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
1 0 1 1 0 0 
1 1 0 1 0 0 
1 1 0 0 1 0 
0 1 0 1 0 1 
, 
1 0 0 0 0 0 
1 1 0 1 0 0 
0 1 1 1 0 0 
1 1 1 0 0 0 
1 0 0 1 1 0 
0 0 1 1 0 1 
, 
0 1 0 1 1 0 
1 0 0 1 1 0 
1 1 1 1 1 0 
1 0 1 0 1 0 
0 1 0 0 0 0 
0 1 1 0 0 1 
, 
1 1 1 1 0 1 
0 1 1 0 0 1 
0 0 1 1 0 1 
0 1 0 1 0 1 
1 0 1 0 1 0 
1 0 0 0 0 0 
)
acting on the columns of the generator matrix as follows (in order):
(6, 18)(19, 20)(21, 22)(23, 24), 
(6, 19)(18, 20)(21, 23)(22, 24), 
(6, 21)(18, 22)(19, 23)(20, 24), 
(5, 16)(11, 17)(12, 14)(13, 15), 
(5, 15)(11, 14)(12, 17)(13, 16), 
(5, 14)(11, 15)(12, 16)(13, 17), 
(5, 23)(6, 16)(11, 24)(12, 21)(13, 22)(14, 19)(15, 20)(17, 18), 
(4, 8)(5, 12)(6, 18)(9, 10)(11, 13)(14, 17)(15, 16)(19, 20), 
(4, 9)(5, 11)(6, 19)(8, 10)(12, 13)(14, 17)(15, 16)(18, 20), 
(3, 10, 7, 9)(4, 8)(5, 11)(6, 21, 18, 22)(12, 16, 13, 17)(19, 20), 
(2, 10, 3, 7, 4, 9, 8)(5, 16, 13, 12, 15, 17, 14)(6, 22, 21, 20, 18, 19, 23), 
(1, 11, 10, 15)(2, 5, 9, 14)(3, 13, 8, 17)(4, 16, 7, 12)(6, 20)(18, 19), 
(1, 6, 10, 24)(2, 19, 7, 23, 3, 21, 9, 22, 4, 18, 8, 20)(5, 14, 15, 17, 13, 12)(11, 16)
orbits: { 1, 15, 24, 13, 5, 11, 20, 16, 12, 10, 14, 23, 22, 17, 3, 2, 19, 18, 21, 6, 8, 4, 7, 9 }

code no       2:
================
1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 0 1 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 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
1 0 1 0 1 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 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
1 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
0 1 0 1 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 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
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 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
the automorphism group has order 2688
and is strongly generated by the following 5 elements:
(
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
1 1 0 1 0 0 
1 1 0 0 1 0 
1 1 0 0 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
0 1 1 1 0 0 
0 1 1 0 1 0 
0 1 1 0 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 0 1 0 0 
1 1 1 0 0 0 
1 1 0 0 1 0 
1 1 0 0 0 1 
, 
1 0 0 0 0 0 
0 1 1 1 0 0 
1 1 1 0 0 0 
0 1 0 0 0 0 
1 0 1 0 1 0 
1 0 1 0 0 1 
, 
1 0 1 0 1 0 
0 1 1 0 1 0 
0 0 0 0 1 0 
0 1 0 1 1 0 
0 1 0 0 0 0 
0 1 1 0 0 1 
)
acting on the columns of the generator matrix as follows (in order):
(4, 8)(5, 11)(6, 18)(9, 10)(12, 13)(19, 20), 
(4, 10)(5, 13)(6, 20)(8, 9)(11, 12)(18, 19), 
(3, 8, 7, 4)(5, 11)(6, 18)(9, 10)(12, 14, 13, 15)(19, 21, 20, 22), 
(2, 4, 7, 3, 9, 8, 10)(5, 16, 13, 14, 15, 11, 12)(6, 23, 20, 21, 22, 18, 19), 
(1, 11, 7, 12)(2, 5, 3, 13)(4, 16, 10, 15)(6, 20)(8, 17, 9, 14)(18, 19)
orbits: { 1, 12, 13, 11, 15, 7, 5, 14, 16, 3, 10, 8, 4, 2, 9, 17 }, { 6, 18, 20, 19, 22, 21, 23 }, { 24 }

code no       3:
================
1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 0 1 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 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
1 0 1 0 1 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 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
1 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
0 1 0 1 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 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
0 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
the automorphism group has order 6144
and is strongly generated by the following 9 elements:
(
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
0 0 0 1 0 0 
0 0 0 0 1 0 
1 1 0 0 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
0 0 0 1 0 0 
1 1 0 0 1 0 
1 1 0 0 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
1 0 1 1 0 0 
0 1 1 0 1 0 
0 1 1 0 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
1 1 0 1 0 0 
1 1 0 0 1 0 
1 1 0 0 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
1 0 1 0 1 0 
0 1 1 1 0 0 
0 1 1 0 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
1 0 1 1 0 0 
1 1 0 1 0 0 
0 1 0 1 1 0 
0 1 0 1 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 1 1 0 1 0 
0 1 0 1 1 0 
0 0 0 0 1 0 
0 1 0 0 1 1 
, 
0 0 1 1 1 0 
1 1 1 1 1 0 
1 0 0 1 1 0 
0 0 0 0 1 0 
0 0 0 1 0 0 
1 0 1 0 0 1 
, 
0 0 0 1 0 0 
1 1 0 1 0 0 
1 0 1 1 0 0 
1 1 1 0 0 0 
1 1 1 1 1 0 
0 1 1 0 0 1 
)
acting on the columns of the generator matrix as follows (in order):
(6, 18)(19, 20)(21, 22)(23, 24), 
(5, 11)(6, 18)(12, 13)(14, 15)(16, 17)(19, 20)(21, 22), 
(4, 9)(5, 13)(6, 20)(8, 10)(11, 12)(14, 15)(16, 17)(18, 19)(21, 22), 
(4, 8)(5, 11)(6, 18)(9, 10)(12, 13)(19, 20), 
(4, 13, 8, 12)(5, 9, 11, 10)(6, 20)(14, 15)(16, 17)(18, 19)(21, 23, 22, 24), 
(3, 10, 7, 9)(4, 8)(5, 14, 11, 15)(6, 21, 18, 22)(12, 13)(19, 20), 
(3, 13)(4, 15)(6, 24)(7, 12)(8, 14)(18, 23), 
(1, 16)(2, 17)(3, 14)(4, 5)(6, 19)(7, 15)(8, 11)(9, 12)(10, 13)(18, 20), 
(1, 10, 7, 4)(2, 9, 3, 8)(5, 14, 13, 17)(6, 20)(11, 15, 12, 16)(18, 19)
orbits: { 1, 16, 4, 17, 12, 9, 8, 15, 5, 7, 2, 13, 11, 10, 14, 3 }, { 6, 18, 20, 22, 24, 19, 21, 23 }

code no       4:
================
1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 0 1 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 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
1 0 1 0 1 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 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
1 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
0 1 0 1 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 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
the automorphism group has order 512
and is strongly generated by the following 8 elements:
(
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
0 0 0 1 0 0 
1 1 0 0 1 0 
1 1 0 0 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
0 0 0 1 0 0 
0 1 1 0 1 0 
1 1 0 0 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
1 1 0 1 0 0 
1 1 0 0 1 0 
1 1 0 0 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
1 0 1 1 0 0 
0 1 1 0 1 0 
0 1 1 0 0 1 
, 
1 0 0 0 0 0 
0 0 1 0 0 0 
0 1 0 0 0 0 
1 0 1 0 1 0 
0 0 0 1 0 0 
0 0 0 0 0 1 
, 
1 1 1 0 0 0 
0 0 1 0 0 0 
0 1 0 0 0 0 
0 1 1 1 0 0 
1 0 1 0 1 0 
1 1 0 0 0 1 
, 
0 0 0 1 0 0 
1 1 0 1 0 0 
1 0 1 1 0 0 
1 0 0 0 0 0 
0 1 0 1 1 0 
1 1 0 0 0 1 
, 
0 0 1 1 1 0 
1 1 1 1 1 0 
1 0 0 1 1 0 
1 1 0 0 1 0 
1 1 0 1 0 0 
0 1 1 0 0 1 
)
acting on the columns of the generator matrix as follows (in order):
(5, 11)(6, 18)(12, 13)(14, 15)(16, 17)(19, 20)(21, 22), 
(5, 13)(6, 18)(11, 12)(14, 17)(15, 16)(19, 20)(21, 22)(23, 24), 
(4, 8)(5, 11)(6, 18)(9, 10)(12, 13)(19, 20), 
(4, 9)(5, 13)(6, 20)(8, 10)(11, 12)(14, 15)(16, 17)(18, 19)(21, 22), 
(2, 3)(4, 5, 8, 12)(9, 11, 10, 13)(14, 15, 17, 16)(18, 19)(21, 23, 22, 24), 
(1, 7)(2, 3)(4, 10)(5, 12)(6, 18)(8, 9)(11, 13)(14, 16)(15, 17)(19, 20)(21, 22), 
(1, 4)(2, 8)(3, 9)(5, 15)(6, 18)(7, 10)(11, 14)(12, 17)(13, 16)(19, 20)(21, 22), 
(1, 16)(2, 17)(3, 14)(4, 11)(5, 8)(6, 20)(7, 15)(9, 13)(10, 12)(18, 19)
orbits: { 1, 7, 4, 16, 10, 15, 8, 9, 12, 11, 17, 14, 13, 5, 2, 3 }, { 6, 18, 20, 19 }, { 21, 22, 24, 23 }

code no       5:
================
1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 0 1 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 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
1 0 1 0 1 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 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
1 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
0 1 0 1 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 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
0 1 0 1 0 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
0 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
the automorphism group has order 96
and is strongly generated by the following 6 elements:
(
1 0 0 0 0 0 
0 1 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 1 0 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
0 1 1 1 0 0 
0 1 1 0 1 0 
0 1 1 0 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
1 0 1 1 0 0 
1 0 1 0 1 0 
1 0 1 0 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
1 1 0 1 0 0 
0 1 1 1 0 0 
1 0 0 1 1 0 
1 0 0 1 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
1 1 1 0 0 0 
1 1 0 1 0 0 
0 0 0 0 1 0 
0 0 0 0 0 1 
, 
0 1 0 0 0 0 
1 0 0 0 0 0 
1 0 1 1 0 0 
1 1 0 1 0 0 
0 1 0 1 1 0 
0 1 0 1 0 1 
)
acting on the columns of the generator matrix as follows (in order):
(5, 6)(11, 17)(12, 18)(13, 19)(14, 20)(15, 21)(16, 22), 
(4, 10)(5, 13)(6, 19)(8, 9)(11, 12)(17, 18), 
(4, 9)(5, 12)(6, 18)(8, 10)(11, 13)(17, 19), 
(3, 9, 8)(4, 7, 10)(5, 13, 14)(6, 19, 20)(11, 12, 15)(17, 18, 21), 
(3, 7)(4, 8)(12, 13)(14, 15)(18, 19)(20, 21), 
(1, 2)(3, 9)(4, 8)(5, 15)(6, 21)(7, 10)(11, 14)(17, 20)(23, 24)
orbits: { 1, 2 }, { 3, 8, 7, 9, 10, 4 }, { 5, 6, 13, 12, 14, 15, 19, 18, 20, 21, 11, 17 }, { 16, 22 }, { 23, 24 }

code no       6:
================
1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 0 1 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 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
1 0 1 0 1 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 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
1 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
0 1 0 1 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 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
1 0 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 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
the automorphism group has order 72
and is strongly generated by the following 5 elements:
(
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 0 1 0 0 
0 0 1 0 0 0 
0 0 0 0 1 0 
0 0 0 0 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 1 0 0 
0 0 0 0 0 1 
, 
1 0 0 0 0 0 
0 0 0 1 0 0 
0 1 0 0 0 0 
0 0 0 0 1 0 
0 0 1 0 0 0 
0 0 0 0 0 1 
, 
1 1 1 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
1 0 1 0 1 0 
1 1 0 1 0 0 
0 1 1 0 0 1 
, 
0 1 0 0 0 0 
1 1 1 0 0 0 
1 0 0 0 0 0 
0 0 0 0 1 0 
1 1 0 1 0 0 
1 1 0 0 0 1 
)
acting on the columns of the generator matrix as follows (in order):
(3, 4)(7, 8)(12, 14)(13, 15)(18, 20)(19, 21)(23, 24), 
(2, 3)(4, 5)(8, 12)(9, 11)(10, 13)(15, 16)(17, 18)(20, 22)(21, 23), 
(2, 3, 5, 4)(7, 12, 14, 8)(9, 11)(10, 13, 16, 15)(17, 18, 22, 20)(19, 23, 24, 21), 
(1, 7)(4, 12)(5, 8)(6, 19)(9, 13)(10, 11)(15, 16)(20, 23)(21, 22), 
(1, 3, 7, 2)(4, 12, 8, 5)(6, 18, 19, 17)(9, 13, 10, 11)(15, 16)(20, 23, 21, 22)
orbits: { 1, 7, 2, 8, 3, 4, 12, 14, 5 }, { 6, 19, 17, 21, 18, 20, 23, 24, 22 }, { 9, 11, 13, 10, 15, 16 }

code no       7:
================
1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 0 1 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 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
1 0 1 0 1 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 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
1 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
0 1 0 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
0 0 1 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
1 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
the automorphism group has order 1152
and is strongly generated by the following 8 elements:
(
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
0 0 0 1 0 0 
1 1 0 0 1 0 
1 1 0 0 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
0 0 0 1 0 0 
1 1 0 0 0 1 
1 1 0 0 1 0 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
1 0 1 1 0 0 
1 0 1 0 1 0 
1 0 1 0 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 0 1 0 0 
0 0 1 0 0 0 
1 1 0 0 1 0 
1 1 0 0 0 1 
, 
1 0 0 0 0 0 
1 0 0 0 1 1 
1 0 1 1 0 0 
0 0 1 0 0 0 
1 0 1 0 0 1 
0 1 1 0 0 1 
, 
1 1 0 1 0 0 
0 0 0 1 0 0 
0 1 0 0 0 0 
1 1 1 0 0 0 
0 1 0 1 1 0 
1 0 0 1 0 1 
, 
1 0 1 1 1 1 
1 0 1 1 0 0 
0 0 1 0 1 1 
1 0 0 0 1 1 
0 1 0 1 0 1 
1 0 0 1 1 0 
, 
1 0 0 1 1 0 
1 0 1 0 1 0 
0 1 0 1 1 0 
1 0 0 1 0 1 
0 0 1 0 0 0 
1 0 1 1 0 0 
)
acting on the columns of the generator matrix as follows (in order):
(5, 11)(6, 16)(12, 13)(14, 15)(17, 18)(19, 20), 
(5, 16)(6, 11)(12, 18)(13, 17)(14, 20)(15, 19), 
(4, 9)(5, 12)(6, 17)(8, 10)(11, 13)(16, 18)(23, 24), 
(3, 4)(5, 11)(6, 16)(7, 8)(12, 15)(13, 14)(17, 20)(18, 19)(22, 23), 
(2, 21)(3, 4, 9)(5, 15, 18, 6, 14, 13, 16, 19, 12, 11, 20, 17)(7, 23, 10, 22, 8, 24), 
(1, 7, 4, 2, 3, 8)(5, 13, 14, 11, 12, 15)(6, 17, 19)(9, 10)(16, 18, 20)(21, 22, 23), 
(1, 8, 24)(2, 23, 9)(3, 7, 22)(4, 10, 21)(5, 17, 20)(6, 18, 14)(11, 13, 15)(12, 19, 16), 
(1, 16, 24, 19, 4, 11, 22, 14)(2, 18, 10, 17, 8, 13, 7, 12)(3, 5, 21, 20, 9, 6, 23, 15)
orbits: { 1, 8, 24, 14, 10, 7, 22, 3, 17, 23, 16, 15, 20, 13, 6, 18, 9, 4, 21, 11, 2, 5, 19, 12 }

code no       8:
================
1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 0 1 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 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
1 0 1 0 1 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 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
1 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
0 1 0 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
0 0 1 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
the automorphism group has order 192
and is strongly generated by the following 7 elements:
(
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
0 0 0 1 0 0 
1 1 0 0 0 1 
1 1 0 0 1 0 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
0 0 0 1 0 0 
1 1 0 0 1 0 
1 1 0 0 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
0 1 1 1 0 0 
1 0 1 0 1 0 
1 0 1 0 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 0 1 0 0 
0 0 1 0 0 0 
1 1 0 0 1 0 
1 1 0 0 0 1 
, 
1 1 1 0 0 0 
0 0 1 0 0 0 
0 1 0 0 0 0 
1 1 0 1 0 0 
0 1 1 0 1 0 
1 0 1 0 0 1 
, 
1 1 0 1 0 0 
0 0 0 1 0 0 
0 1 0 0 0 0 
1 1 1 0 0 0 
0 1 0 1 1 0 
1 0 0 1 0 1 
, 
0 1 1 1 0 0 
1 0 1 1 0 0 
1 0 0 0 0 0 
0 0 1 0 0 0 
0 1 0 1 0 1 
0 1 0 1 1 0 
)
acting on the columns of the generator matrix as follows (in order):
(5, 16)(6, 11)(12, 18)(13, 17)(14, 20)(15, 19), 
(5, 11)(6, 16)(12, 13)(14, 15)(17, 18)(19, 20), 
(4, 10)(5, 12)(6, 17)(8, 9)(11, 13)(14, 15)(16, 18)(19, 20)(23, 24), 
(3, 4)(5, 11)(6, 16)(7, 8)(12, 15)(13, 14)(17, 20)(18, 19)(22, 23), 
(1, 7)(2, 3)(4, 8)(5, 13)(6, 17)(9, 10)(11, 12)(14, 15)(16, 18)(21, 22), 
(1, 7, 4, 2, 3, 8)(5, 13, 14, 11, 12, 15)(6, 17, 19)(9, 10)(16, 18, 20)(21, 22, 23), 
(1, 3, 4, 10)(2, 7, 8, 9)(5, 19, 11, 20)(6, 14, 16, 15)(12, 17)(13, 18)(21, 22, 23, 24)
orbits: { 1, 7, 8, 10, 2, 9, 4, 3 }, { 5, 16, 11, 12, 13, 15, 20, 6, 18, 14, 19, 17 }, { 21, 22, 23, 24 }