the 8 isometry classes of irreducible [23,10,8]_2 codes are:

code no       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 1 1 1 1 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
1 1 1 1 0 0 0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0
1 1 0 0 1 1 0 1 1 0 1 0 0 0 0 0 1 0 0 0 0 0 0
1 0 1 0 1 0 1 1 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0
1 0 0 1 0 1 1 0 1 1 1 0 0 0 0 0 0 0 1 0 0 0 0
1 0 0 1 1 0 1 1 1 0 0 1 0 0 0 0 0 0 0 1 0 0 0
1 1 0 0 0 1 1 1 0 1 0 1 0 0 0 0 0 0 0 0 1 0 0
1 0 1 0 1 1 0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 1 0
1 0 1 1 0 1 0 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 1
the automorphism group has order 3840
and is strongly generated by the following 9 elements:
(
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 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 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 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 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 1 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 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 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 1 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 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 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 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 1 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 1 0 1 1 0 0 1 1 0 1 0 
1 1 0 0 0 1 1 1 0 1 0 1 0 
1 0 0 1 1 0 1 1 1 0 0 1 0 
1 1 0 0 1 1 0 1 1 0 1 0 0 
1 0 0 1 0 1 1 0 1 1 1 0 0 
1 0 1 0 1 0 1 1 0 1 1 0 0 
1 1 1 1 0 0 0 1 1 1 0 0 0 
1 1 1 1 1 1 1 0 0 0 0 0 0 
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 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 1 0 0 0 0 0 0 0 0 0 
1 1 0 0 0 1 1 1 0 1 0 1 0 
1 0 1 0 1 1 0 0 1 1 0 1 0 
0 0 0 0 0 0 0 0 0 0 0 1 0 
1 0 1 0 1 0 1 1 0 1 1 0 0 
0 0 0 0 0 0 0 0 0 0 1 0 0 
1 1 0 0 1 1 0 1 1 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 
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 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 1 0 0 0 0 0 0 0 0 0 
1 0 0 1 1 0 1 1 1 0 0 1 0 
0 0 0 0 0 0 0 0 0 0 0 1 0 
1 0 1 0 1 1 0 0 1 1 0 1 0 
0 0 0 0 0 0 0 0 0 0 1 0 0 
1 0 1 0 1 0 1 1 0 1 1 0 0 
1 0 0 1 0 1 1 0 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 
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 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 
1 0 1 1 0 1 0 1 0 0 1 1 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 0 
1 0 1 0 1 1 0 0 1 1 0 1 0 
1 0 0 1 1 0 1 1 1 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 0 
1 0 0 1 0 1 1 0 1 1 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 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 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 
1 1 1 1 0 0 0 1 1 1 0 0 0 
0 0 0 0 0 0 0 0 1 0 0 0 0 
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 1 0 0 0 0 0 0 0 0 
1 1 0 0 1 1 0 1 1 0 1 0 0 
1 1 0 0 0 1 1 1 0 1 0 1 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 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 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 
1 0 1 0 1 1 0 0 1 1 0 1 0 
1 0 0 1 1 0 1 1 1 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 
1 1 1 1 0 0 0 1 1 1 0 0 0 
0 0 0 0 0 1 0 0 0 0 0 0 0 
1 1 0 0 1 1 0 1 1 0 1 0 0 
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 1 1 1 1 1 1 0 0 0 0 0 0 
1 0 1 0 1 1 0 0 1 1 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 0 0 0 0 0 0 0 1 0 
0 0 1 0 0 0 0 0 0 0 0 0 0 
1 0 1 0 1 0 1 1 0 1 1 0 0 
0 0 0 0 0 0 0 0 0 0 1 0 0 
1 0 1 1 0 1 0 1 0 0 1 1 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 
)
acting on the columns of the generator matrix as follows (in order):
(13, 14), 
(5, 10)(6, 8)(7, 9)(11, 12)(15, 16)(17, 21)(18, 22)(19, 20), 
(5, 22)(6, 21)(7, 20)(8, 17)(9, 19)(10, 18)(11, 16)(12, 15)(13, 14), 
(5, 21)(6, 22)(7, 12)(8, 18)(9, 11)(10, 17)(13, 14)(15, 20)(16, 19), 
(5, 20)(6, 12)(7, 22)(8, 11)(9, 18)(10, 19)(13, 14)(15, 21)(16, 17), 
(4, 23)(5, 6, 19, 11)(7, 9, 18, 22)(8, 10, 12, 20)(15, 21, 17, 16), 
(3, 4)(5, 10)(6, 16)(7, 9)(8, 15)(11, 17)(12, 21), 
(2, 4, 3)(5, 17, 12)(6, 11, 22)(7, 19, 20)(8, 16, 10)(13, 14)(15, 18, 21), 
(2, 21, 17, 16, 15)(3, 7, 5, 20, 22)(4, 11, 9, 18, 8)(6, 19, 23, 10, 12)
orbits: { 1 }, { 2, 3, 15, 4, 22, 16, 12, 20, 21, 8, 23, 18, 5, 6, 7, 11, 19, 17, 10, 9 }, { 13, 14 }

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

code no       3:
================
1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0
1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
1 1 1 1 0 0 0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0
1 1 0 0 1 1 0 1 1 0 1 0 0 0 0 0 1 0 0 0 0 0 0
1 0 1 0 1 0 1 1 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0
1 0 0 1 0 1 1 0 1 1 1 0 0 0 0 0 0 0 1 0 0 0 0
1 0 0 1 1 0 1 1 1 0 0 1 0 0 0 0 0 0 0 1 0 0 0
1 1 0 0 0 1 1 1 0 1 0 1 0 0 0 0 0 0 0 0 1 0 0
1 0 1 0 0 1 1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0
1 0 0 1 1 1 0 1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 1
the automorphism group has order 144
and is strongly generated by the following 6 elements:
(
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 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 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 1 0 0 0 0 0 0 
1 0 0 1 0 1 1 0 1 1 1 0 0 
1 0 1 0 1 0 1 1 0 1 1 0 0 
1 1 0 0 1 1 0 1 1 0 1 0 0 
1 1 1 1 0 0 0 1 1 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 1 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 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 1 0 0 
1 1 0 0 1 1 0 1 1 0 1 0 0 
1 0 1 0 1 0 1 1 0 1 1 0 0 
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 1 0 0 0 0 0 0 0 
1 1 1 1 0 0 0 1 1 1 0 0 0 
1 1 0 0 0 1 1 1 0 1 0 1 0 
1 0 1 0 0 1 1 1 1 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 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 1 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 1 0 0 0 0 0 0 
1 0 0 1 0 1 1 0 1 1 1 0 0 
1 0 1 0 1 0 1 1 0 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 1 0 0 0 
1 0 0 1 1 0 1 1 1 0 0 1 0 
1 0 1 0 0 1 1 1 1 0 0 0 1 
, 
1 0 0 0 0 0 0 0 0 0 0 0 0 
1 1 1 1 1 1 1 0 0 0 0 0 0 
1 0 0 1 0 1 1 0 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 1 0 0 0 0 
1 0 1 0 1 0 1 1 0 1 1 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 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 1 0 
1 0 1 0 0 1 1 1 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 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 1 0 0 0 
0 0 0 0 0 0 0 0 1 0 0 0 0 
1 1 1 1 0 0 0 1 1 1 0 0 0 
1 0 0 1 0 1 1 0 1 1 1 0 0 
0 0 0 0 0 0 0 0 0 0 1 0 0 
1 0 1 0 1 0 1 1 0 1 1 0 0 
0 0 0 0 0 1 0 0 0 0 0 0 0 
1 1 0 0 0 1 1 1 0 1 0 1 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 0 0 1 1 1 0 1 0 1 0 0 1 
1 0 1 0 0 1 1 1 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 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 0 0 0 0 0 0 0 0 0 1 0 
1 1 0 0 1 1 0 1 1 0 1 0 0 
0 0 0 0 0 0 0 0 1 0 0 0 0 
1 0 1 0 1 0 1 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 0 1 0 0 0 0 0 
)
acting on the columns of the generator matrix as follows (in order):
(8, 19)(9, 18)(10, 17)(11, 16)(12, 13)(20, 22)(21, 23), 
(5, 16, 11)(6, 10, 17)(7, 9, 18)(8, 19, 15)(12, 20, 21)(13, 23, 22), 
(3, 4)(5, 6)(8, 19)(9, 18)(10, 11)(12, 20)(13, 22)(16, 17), 
(2, 15)(3, 19)(4, 8)(5, 9)(6, 18)(10, 11)(13, 22), 
(2, 3, 4)(5, 18, 10)(6, 11, 9)(7, 17, 16)(8, 15, 19)(12, 20, 21), 
(1, 14)(2, 21, 15, 23)(3, 12, 8, 13, 4, 20, 19, 22)(5, 16, 18, 11, 6, 17, 9, 10)
orbits: { 1, 14 }, { 2, 15, 4, 23, 19, 8, 21, 3, 13, 20, 12, 22 }, { 5, 11, 6, 9, 10, 16, 18, 17, 7 }

code no       4:
================
1 1 1 1 1 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
1 1 1 1 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0
1 1 0 0 1 1 0 1 1 0 1 0 0 0 0 1 0 0 0 0 0 0 0
1 0 1 0 1 0 1 1 0 1 1 0 0 0 0 0 1 0 0 0 0 0 0
1 0 0 1 0 1 1 0 1 1 1 0 0 0 0 0 0 1 0 0 0 0 0
0 1 1 0 1 0 1 1 1 0 0 1 0 0 0 0 0 0 1 0 0 0 0
1 1 0 0 0 1 1 1 0 1 0 1 0 0 0 0 0 0 0 1 0 0 0
0 1 0 1 1 1 0 0 1 1 0 1 0 0 0 0 0 0 0 0 1 0 0
0 0 0 1 1 1 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 1 0
0 1 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 1
the automorphism group has order 80640
and is strongly generated by the following 10 elements:
(
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 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 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 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 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 1 0 0 
0 0 0 0 0 0 0 0 0 0 0 1 0 
0 1 0 1 0 1 1 1 1 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 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 0 0 0 0 0 0 
0 0 0 0 1 0 0 0 0 0 0 0 0 
1 1 1 1 1 1 1 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 1 0 0 0 
1 1 1 1 0 0 0 1 1 1 0 0 0 
0 0 0 0 0 0 0 1 0 0 0 0 0 
1 0 0 1 0 1 1 0 1 1 1 0 0 
0 1 1 0 1 0 1 1 1 0 0 1 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 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 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 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 0 0 0 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 1 0 0 0 0 
1 1 0 0 1 1 0 1 1 0 1 0 0 
1 1 0 0 0 1 1 1 0 1 0 1 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 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 1 0 0 0 0 0 0 0 0 0 
1 1 1 1 0 0 0 1 1 1 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 1 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 0 0 0 0 0 0 
0 1 1 0 1 0 1 1 1 0 0 1 0 
1 0 0 1 0 1 1 0 1 1 1 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 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 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 1 0 1 1 0 1 1 1 0 0 
1 1 0 0 1 1 0 1 1 0 1 0 0 
0 1 0 1 1 1 0 0 1 1 0 1 0 
0 0 0 0 0 0 0 0 0 0 0 1 0 
1 1 0 0 0 1 1 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 1 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 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 1 1 1 1 1 0 0 1 1 0 
0 0 0 0 0 0 0 0 1 0 0 0 0 
1 0 1 0 1 0 1 1 0 1 1 0 0 
0 1 0 1 1 1 0 0 1 1 0 1 0 
1 1 1 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 1 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 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 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 0 0 0 0 0 
1 1 1 1 1 1 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 
1 1 0 0 1 1 0 1 1 0 1 0 0 
1 0 0 1 0 1 1 0 1 1 1 0 0 
0 0 0 0 0 0 0 0 0 1 0 0 0 
1 1 0 0 0 1 1 1 0 1 0 1 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 1 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 
1 1 1 1 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 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 1 0 0 0 0 0 0 
1 1 1 1 1 1 1 0 0 0 0 0 0 
1 0 1 0 1 0 1 1 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 1 
, 
1 0 0 0 0 0 0 0 0 0 0 0 0 
1 1 1 1 1 1 1 0 0 0 0 0 0 
0 1 0 1 1 1 0 0 1 1 0 1 0 
1 1 0 0 1 1 0 1 1 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 1 0 0 0 0 
0 0 0 1 1 1 1 1 0 0 1 1 0 
0 0 0 1 0 0 0 0 0 0 0 0 0 
0 1 1 0 1 0 1 1 1 0 0 1 0 
1 0 0 1 0 1 1 0 1 1 1 0 0 
0 0 0 0 0 1 0 0 0 0 0 0 0 
1 1 0 0 0 1 1 1 0 1 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 
1 1 0 0 0 1 1 1 0 1 0 1 0 
0 0 0 0 0 0 0 0 0 0 0 1 0 
0 1 1 0 1 0 1 1 1 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 
1 1 1 1 0 0 0 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 
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 0 0 1 0 1 1 0 1 1 1 0 0 
0 0 0 0 0 0 0 0 0 0 0 0 1 
)
acting on the columns of the generator matrix as follows (in order):
(13, 23), 
(5, 6)(7, 14)(8, 10)(9, 15)(11, 18)(12, 19)(16, 17)(20, 21), 
(5, 7)(6, 14)(8, 15)(9, 10)(11, 16)(12, 20)(17, 18)(19, 21), 
(5, 15)(6, 9)(7, 8)(10, 14)(11, 19)(12, 18)(16, 21)(17, 20), 
(5, 11)(6, 18)(7, 16)(8, 21)(9, 12)(10, 20)(14, 17)(15, 19), 
(4, 22)(5, 14, 8, 9)(6, 12, 10, 17)(7, 11, 15, 21)(16, 20, 19, 18), 
(3, 4)(5, 14, 6, 7)(8, 18, 10, 11)(9, 17, 15, 16)(12, 21, 19, 20), 
(2, 4)(5, 15)(6, 8)(7, 9)(10, 14)(11, 17)(19, 20), 
(2, 17, 18, 10, 22, 7, 15, 14)(3, 20, 12, 16, 4, 8, 5, 21)(6, 11, 19, 9), 
(1, 16, 21)(2, 17, 19, 4, 11, 20)(3, 18, 12)(5, 9, 6, 15, 7, 8)(10, 14)
orbits: { 1, 21, 20, 19, 16, 8, 15, 12, 5, 17, 10, 3, 11, 7, 18, 14, 6, 4, 9, 2, 22 }, { 13, 23 }

code no       5:
================
1 1 1 1 1 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
1 1 1 1 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0
1 1 0 0 1 1 0 1 1 0 1 0 0 0 0 1 0 0 0 0 0 0 0
1 0 1 0 1 0 1 1 0 1 1 0 0 0 0 0 1 0 0 0 0 0 0
1 0 0 1 0 1 1 0 1 1 1 0 0 0 0 0 0 1 0 0 0 0 0
0 1 1 0 1 0 1 1 1 0 0 1 0 0 0 0 0 0 1 0 0 0 0
1 1 0 0 0 1 1 1 0 1 0 1 0 0 0 0 0 0 0 1 0 0 0
0 1 0 1 1 1 0 0 1 1 0 1 0 0 0 0 0 0 0 0 1 0 0
0 0 0 1 1 1 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 1 0
1 0 1 1 1 0 0 0 1 0 1 1 1 0 0 0 0 0 0 0 0 0 1
the automorphism group has order 80640
and is strongly generated by the following 10 elements:
(
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 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 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 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 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 1 0 0 
0 0 0 0 0 0 0 0 0 0 0 1 0 
1 0 1 1 1 0 0 0 1 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 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 1 0 0 0 0 0 0 
1 1 1 1 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 0 0 0 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 1 0 0 0 0 
1 1 0 0 1 1 0 1 1 0 1 0 0 
1 1 0 0 0 1 1 1 0 1 0 1 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 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 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 1 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 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 1 1 0 1 0 1 0 
1 1 0 0 1 1 0 1 1 0 1 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 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 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 1 0 1 1 0 1 1 1 0 0 
1 1 0 0 1 1 0 1 1 0 1 0 0 
0 1 0 1 1 1 0 0 1 1 0 1 0 
0 0 0 0 0 0 0 0 0 0 0 1 0 
1 1 0 0 0 1 1 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 1 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 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 1 0 0 0 0 0 0 0 0 0 
1 0 0 1 0 1 1 0 1 1 1 0 0 
0 0 0 0 0 0 0 0 0 0 1 0 0 
1 0 1 0 1 0 1 1 0 1 1 0 0 
1 1 0 0 0 1 1 1 0 1 0 1 0 
0 1 1 0 1 0 1 1 1 0 0 1 0 
0 1 0 1 1 1 0 0 1 1 0 1 0 
0 0 0 0 0 1 0 0 0 0 0 0 0 
1 1 1 1 0 0 0 1 1 1 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 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 1 1 1 1 1 0 0 1 1 0 
0 1 1 0 1 0 1 1 1 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 
1 1 0 0 1 1 0 1 1 0 1 0 0 
1 1 0 0 0 1 1 1 0 1 0 1 0 
1 1 1 1 0 0 0 1 1 1 0 0 0 
1 0 1 0 1 0 1 1 0 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 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 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 1 0 0 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 1 1 0 1 1 0 0 
1 0 0 1 0 1 1 0 1 1 1 0 0 
1 1 0 0 1 1 0 1 1 0 1 0 0 
1 1 1 1 0 0 0 1 1 1 0 0 0 
0 1 1 0 1 0 1 1 1 0 0 1 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 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 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 1 0 0 0 0 0 0 
0 0 0 0 1 0 0 0 0 0 0 0 0 
1 0 0 1 0 1 1 0 1 1 1 0 0 
1 0 1 0 1 0 1 1 0 1 1 0 0 
1 1 0 0 1 1 0 1 1 0 1 0 0 
1 1 0 0 0 1 1 1 0 1 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 1 
, 
1 0 0 0 0 0 0 0 0 0 0 0 0 
1 0 0 1 0 1 1 0 1 1 1 0 0 
1 1 1 1 0 0 0 1 1 1 0 0 0 
0 0 0 0 1 0 0 0 0 0 0 0 0 
0 1 0 1 1 1 0 0 1 1 0 1 0 
0 0 0 1 1 1 1 1 0 0 1 1 0 
1 1 0 0 0 1 1 1 0 1 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 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 
1 1 0 0 1 1 0 1 1 0 1 0 0 
0 0 0 0 0 0 0 0 0 0 0 0 1 
, 
0 0 0 1 1 1 1 1 0 0 1 1 0 
0 0 0 0 0 0 0 0 0 0 1 0 0 
1 0 1 0 1 0 1 1 0 1 1 0 0 
1 1 0 0 1 1 0 1 1 0 1 0 0 
0 0 0 0 0 1 0 0 0 0 0 0 0 
0 1 0 1 1 1 0 0 1 1 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 
1 1 0 0 0 1 1 1 0 1 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 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 1 
)
acting on the columns of the generator matrix as follows (in order):
(13, 23), 
(5, 7)(6, 14)(8, 15)(9, 10)(11, 16)(12, 20)(17, 18)(19, 21), 
(5, 10)(6, 8)(7, 9)(11, 20)(12, 16)(14, 15)(17, 19)(18, 21), 
(5, 11)(6, 18)(7, 16)(8, 21)(9, 12)(10, 20)(14, 17)(15, 19), 
(5, 18)(6, 11)(7, 17)(8, 20)(9, 19)(10, 21)(12, 15)(14, 16), 
(4, 22)(5, 16, 8, 19)(6, 15, 10, 7)(9, 18, 14, 20)(11, 12, 21, 17), 
(3, 4)(5, 6)(8, 17)(9, 18)(10, 16)(11, 15)(12, 19), 
(2, 4, 3)(5, 7, 6)(8, 19, 18)(9, 12, 17)(10, 21, 16)(11, 15, 20), 
(2, 11, 10, 18)(3, 19, 14, 15)(4, 9, 21, 5)(6, 16, 12, 22)(7, 20), 
(1, 16, 4, 21, 6, 5, 18, 22)(2, 10, 20, 9, 8, 7, 12, 11)(3, 14, 15, 17)
orbits: { 1, 22, 4, 12, 18, 3, 2, 5, 16, 20, 9, 15, 11, 19, 7, 17, 21, 6, 10, 14, 8 }, { 13, 23 }

code no       6:
================
1 1 1 1 1 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
1 1 1 1 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0
1 1 0 0 1 1 0 1 1 0 1 0 0 0 0 1 0 0 0 0 0 0 0
1 0 1 0 1 0 1 1 0 1 1 0 0 0 0 0 1 0 0 0 0 0 0
1 0 0 1 0 1 1 0 1 1 1 0 0 0 0 0 0 1 0 0 0 0 0
0 1 1 0 1 0 1 1 1 0 0 1 0 0 0 0 0 0 1 0 0 0 0
1 1 0 0 0 1 1 1 0 1 0 1 0 0 0 0 0 0 0 1 0 0 0
0 1 0 1 1 1 0 0 1 1 0 1 0 0 0 0 0 0 0 0 1 0 0
1 0 1 0 0 1 1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0
0 1 1 0 1 1 0 1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 1
the automorphism group has order 5760
and is strongly generated by the following 8 elements:
(
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 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 1 0 0 0 0 0 0 0 0 
1 1 1 1 1 1 1 0 0 0 0 0 0 
0 0 0 0 0 1 0 0 0 0 0 0 0 
0 1 0 1 1 1 0 0 1 1 0 1 0 
0 1 1 0 1 0 1 1 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 1 0 0 0 0 0 
1 1 0 0 1 1 0 1 1 0 1 0 0 
0 1 1 0 1 1 0 1 0 1 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 1 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 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 1 0 0 0 0 
0 0 0 0 0 0 0 1 0 0 0 0 0 
1 1 1 1 0 0 0 1 1 1 0 0 0 
1 0 1 0 1 0 1 1 0 1 1 0 0 
0 1 0 1 1 1 0 0 1 1 0 1 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 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 1 0 0 0 0 0 0 0 0 0 
0 1 1 0 1 0 1 1 1 0 0 1 0 
0 0 0 0 0 0 0 0 0 0 0 1 0 
0 1 0 1 1 1 0 0 1 1 0 1 0 
1 1 0 0 1 1 0 1 1 0 1 0 0 
1 0 0 1 0 1 1 0 1 1 1 0 0 
1 0 1 0 1 0 1 1 0 1 1 0 0 
1 1 1 1 0 0 0 1 1 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 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 1 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 0 1 1 0 1 1 1 0 0 
0 0 0 0 0 0 0 0 0 0 1 0 0 
1 0 1 0 1 0 1 1 0 1 1 0 0 
1 1 0 0 0 1 1 1 0 1 0 1 0 
0 1 1 0 1 0 1 1 1 0 0 1 0 
0 1 0 1 1 1 0 0 1 1 0 1 0 
0 0 0 0 0 1 0 0 0 0 0 0 0 
1 1 1 1 0 0 0 1 1 1 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 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 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 1 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 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 1 1 0 1 0 1 0 
1 1 0 0 1 1 0 1 1 0 1 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 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 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 0 0 0 0 0 0 0 
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 1 0 0 1 1 0 1 1 0 1 0 0 
1 0 0 1 0 1 1 0 1 1 1 0 0 
0 0 0 0 0 0 0 1 0 0 0 0 0 
0 1 1 0 1 0 1 1 1 0 0 1 0 
1 0 1 0 0 1 1 1 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 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 
1 1 0 0 0 1 1 1 0 1 0 1 0 
0 1 0 1 1 1 0 0 1 1 0 1 0 
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 1 0 0 0 0 0 0 0 
1 0 1 0 1 0 1 1 0 1 1 0 0 
1 1 1 1 0 0 0 1 1 1 0 0 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 0 0 0 0 0 0 0 0 0 0 1 0 
1 1 0 0 0 1 1 1 0 1 0 1 0 
0 1 1 0 1 0 1 1 1 0 0 1 0 
0 0 0 0 0 1 0 0 0 0 0 0 0 
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 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 1 0 0 0 0 0 0 0 0 0 
1 1 0 0 1 1 0 1 1 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 
)
acting on the columns of the generator matrix as follows (in order):
(6, 7, 14)(8, 11, 21)(9, 18, 19)(10, 16, 12)(13, 22, 23)(15, 17, 20), 
(5, 14)(6, 7)(8, 9)(10, 15)(11, 17)(12, 21)(16, 18)(19, 20), 
(5, 19)(6, 12)(7, 21)(8, 16)(9, 18)(10, 17)(11, 15)(14, 20), 
(5, 18)(6, 11)(7, 17)(8, 20)(9, 19)(10, 21)(12, 15)(14, 16), 
(5, 10)(6, 8)(7, 9)(11, 20)(12, 16)(14, 15)(17, 19)(18, 21), 
(3, 4)(7, 14)(8, 11)(9, 16)(10, 18)(12, 19)(13, 22)(15, 17), 
(2, 3, 4)(5, 15, 12)(6, 10, 20)(7, 9, 21)(8, 19, 14)(11, 16, 17), 
(1, 9, 21)(2, 8, 12)(3, 15, 20)(4, 10, 19)(5, 14, 6)(11, 17, 16)
orbits: { 1, 21, 11, 12, 7, 10, 18, 9, 8, 17, 15, 6, 20, 16, 19, 14, 5, 4, 2, 3 }, { 13, 23, 22 }

code no       7:
================
1 1 1 1 1 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
1 1 1 1 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0
1 1 0 0 1 1 0 1 1 0 1 0 0 0 0 1 0 0 0 0 0 0 0
1 0 1 0 1 0 1 1 0 1 1 0 0 0 0 0 1 0 0 0 0 0 0
1 0 0 1 0 1 1 0 1 1 1 0 0 0 0 0 0 1 0 0 0 0 0
0 1 1 0 1 0 1 1 1 0 0 1 0 0 0 0 0 0 1 0 0 0 0
1 1 0 0 0 1 1 1 0 1 0 1 0 0 0 0 0 0 0 1 0 0 0
0 1 0 1 1 1 0 0 1 1 0 1 0 0 0 0 0 0 0 0 1 0 0
1 0 1 0 0 1 1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0
0 0 0 1 1 1 1 1 0 0 1 1 1 0 0 0 0 0 0 0 0 0 1
the automorphism group has order 3840
and is strongly generated by the following 7 elements:
(
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 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 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 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 1 0 0 0 0 0 
1 1 1 1 0 0 0 1 1 1 0 0 0 
1 1 0 0 1 1 0 1 1 0 1 0 0 
0 1 1 0 1 0 1 1 1 0 0 1 0 
1 0 1 0 0 1 1 1 1 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 1 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 0 1 1 0 1 1 1 0 0 
0 0 0 0 0 0 0 0 0 0 1 0 0 
1 0 1 0 1 0 1 1 0 1 1 0 0 
1 1 0 0 0 1 1 1 0 1 0 1 0 
0 1 1 0 1 0 1 1 1 0 0 1 0 
0 1 0 1 1 1 0 0 1 1 0 1 0 
0 0 0 0 0 1 0 0 0 0 0 0 0 
1 1 1 1 0 0 0 1 1 1 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 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 1 0 0 0 0 0 0 0 0 0 
1 1 1 1 0 0 0 1 1 1 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 1 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 0 0 0 0 0 0 
0 1 1 0 1 0 1 1 1 0 0 1 0 
1 0 0 1 0 1 1 0 1 1 1 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 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 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 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 0 0 0 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 1 0 0 0 0 
1 1 0 0 1 1 0 1 1 0 1 0 0 
1 1 0 0 0 1 1 1 0 1 0 1 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 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 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 0 0 0 0 0 0 0 
1 1 1 1 1 1 1 0 0 0 0 0 0 
1 1 0 0 1 1 0 1 1 0 1 0 0 
0 0 0 0 0 0 0 0 0 0 1 0 0 
1 0 1 0 1 0 1 1 0 1 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 1 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 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 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 1 0 
1 1 0 0 0 1 1 1 0 1 0 1 0 
0 1 0 1 1 1 0 0 1 1 0 1 0 
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 1 0 0 0 0 0 0 0 
1 0 1 0 1 0 1 1 0 1 1 0 0 
1 1 1 1 0 0 0 1 1 1 0 0 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 0 0 0 0 0 0 0 0 0 0 1 0 
1 1 0 0 0 1 1 1 0 1 0 1 0 
0 1 1 0 1 0 1 1 1 0 0 1 0 
0 0 0 0 0 1 0 0 0 0 0 0 0 
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 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 1 0 0 0 0 0 0 0 0 0 
1 1 0 0 1 1 0 1 1 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 
)
acting on the columns of the generator matrix as follows (in order):
(8, 9)(10, 15)(11, 16)(12, 19)(13, 22)(17, 18)(20, 21), 
(5, 18)(6, 11)(7, 17)(8, 20)(9, 19)(10, 21)(12, 15)(14, 16), 
(5, 15)(6, 9)(7, 8)(10, 14)(11, 19)(12, 18)(16, 21)(17, 20), 
(5, 7)(6, 14)(8, 15)(9, 10)(11, 16)(12, 20)(17, 18)(19, 21), 
(3, 4)(7, 14)(8, 16)(9, 11)(10, 17)(15, 18)(20, 21), 
(2, 3, 4)(5, 15, 12)(6, 10, 20)(7, 9, 21)(8, 19, 14)(11, 16, 17), 
(1, 9, 21)(2, 8, 12)(3, 15, 20)(4, 10, 19)(5, 14, 6)(11, 17, 16)
orbits: { 1, 21, 20, 10, 16, 19, 9, 8, 17, 12, 15, 14, 6, 4, 11, 7, 2, 18, 5, 3 }, { 13, 22 }, { 23 }

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