the 9 isometry classes of irreducible [22,9,8]_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
1 1 1 1 1 1 1 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 0 0 1 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
1 0 1 0 1 0 1 1 0 1 1 0 0 0 0 0 0 1 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
1 0 0 1 1 0 1 1 1 0 0 1 0 0 0 0 0 0 0 1 0 0
1 1 0 0 0 1 1 1 0 1 0 1 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 1
the automorphism group has order 576
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 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 1 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 
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 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 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 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 0 0 0 1 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 
0 0 0 0 0 0 0 1 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 0 0 0 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 
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 1 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 
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 
, 
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 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 
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 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 
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 0 0 0 1 1 1 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 
)
acting on the columns of the generator matrix as follows (in order):
(13, 14), 
(6, 15, 7)(8, 12, 19)(9, 21, 11)(10, 22, 18)(16, 20, 17), 
(5, 10, 18)(6, 16, 19)(7, 8, 11)(9, 17, 15)(12, 20, 21), 
(5, 22)(6, 21)(7, 20)(8, 17)(9, 19)(10, 18)(11, 16)(12, 15)(13, 14), 
(5, 8, 12)(6, 16, 22)(7, 9, 20)(10, 21, 15)(11, 18, 17), 
(3, 4)(7, 15)(8, 17)(9, 11)(10, 18)(12, 20)(16, 19), 
(2, 3, 4)(5, 10, 18)(6, 8, 17)(7, 9, 19)(11, 15, 16)(13, 14)
orbits: { 1 }, { 2, 4, 3 }, { 5, 18, 22, 12, 10, 11, 16, 8, 21, 15, 20, 17, 9, 6, 19, 7 }, { 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
1 1 1 1 1 1 1 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 0 0 1 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
1 0 1 0 1 0 1 1 0 1 1 0 0 0 0 0 0 1 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
1 0 0 1 1 0 1 1 1 0 0 1 0 0 0 0 0 0 0 1 0 0
1 1 0 0 0 1 1 1 0 1 0 1 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 1
the automorphism group has order 36
and is strongly generated by the following 4 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 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 
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 0 1 1 0 1 1 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 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 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 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 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 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 
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 1 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 1 
)
acting on the columns of the generator matrix as follows (in order):
(5, 6)(7, 15)(8, 16)(9, 10)(11, 18)(13, 22)(17, 19), 
(3, 4)(7, 15)(8, 17)(9, 11)(10, 18)(12, 20)(16, 19), 
(2, 3, 4)(5, 18, 10)(6, 11, 9)(7, 17, 16)(8, 15, 19)(12, 20, 21), 
(2, 19)(3, 15)(4, 8)(5, 10)(7, 17)(9, 11)(12, 21)
orbits: { 1 }, { 2, 4, 19, 3, 8, 17, 16, 15, 7 }, { 5, 6, 10, 9, 18, 11 }, { 12, 20, 21 }, { 13, 22 }, { 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
1 1 1 1 1 1 1 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 0 0 1 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
1 0 1 0 1 0 1 1 0 1 1 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 1 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
1 0 1 1 0 1 0 1 0 0 1 1 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 1
the automorphism group has order 384
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 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 0 0 0 1 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 
0 0 0 0 0 0 1 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 
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 1 0 0 0 0 0 0 0 0 0 
1 0 1 1 0 1 0 1 0 0 1 1 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 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 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 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 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 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 
0 0 0 0 0 0 1 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 1 0 0 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 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 1 0 0 0 1 1 1 0 1 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 0 0 0 0 0 0 0 0 0 1 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 0 0 0 0 0 0 0 0 0 0 
1 1 1 1 0 0 0 1 1 1 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 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 1 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 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 1 0 0 0 
1 0 1 0 0 1 1 1 1 0 0 0 1 
1 0 1 1 0 1 0 1 0 0 1 1 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 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 
)
acting on the columns of the generator matrix as follows (in order):
(5, 9)(6, 16)(7, 10)(8, 15)(11, 20)(12, 17)(18, 19), 
(3, 20)(4, 5)(6, 21)(7, 18)(8, 15)(10, 12)(17, 19), 
(3, 16, 20, 21, 11, 6)(4, 9, 5)(7, 10, 12, 18, 19, 17)(8, 15)(13, 22), 
(2, 10, 5, 19)(3, 21, 12, 17)(4, 6, 9, 20)(7, 18, 16, 11)(8, 15), 
(1, 14)(2, 21, 9, 12)(3, 5, 17, 4)(6, 18, 10, 7)(8, 22)(11, 19, 16, 20)(13, 15)
orbits: { 1, 14 }, { 2, 19, 12, 18, 17, 5, 11, 10, 21, 9, 7, 6, 4, 3, 20, 16 }, { 8, 15, 22, 13 }

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

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
1 1 1 1 0 0 0 1 1 1 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 1 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
1 0 0 1 0 1 1 0 1 1 1 0 0 0 0 0 0 1 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
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 1 1 0 0 1 1 0 1 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 1
the automorphism group has order 7680
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 
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 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 
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 
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 0 1 0 
0 1 1 0 1 0 1 1 1 0 0 1 0 
1 1 0 0 0 1 1 1 0 1 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 1 0 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 
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 
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 
0 0 0 0 0 0 0 0 0 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 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 0 1 1 0 1 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 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 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 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 
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 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 
1 1 0 0 0 1 1 1 0 1 0 1 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 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 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):
(13, 22), 
(8, 9)(10, 15)(11, 16)(12, 19)(17, 18)(20, 21), 
(5, 12)(6, 19)(7, 20)(8, 17)(9, 11)(10, 16)(14, 21)(15, 18), 
(5, 7)(6, 14)(8, 10)(9, 15)(12, 21)(19, 20), 
(5, 18, 7, 17)(6, 11, 14, 16)(8, 19, 15, 21)(9, 20, 10, 12), 
(3, 4)(7, 14)(8, 11)(9, 16)(10, 18)(12, 19)(15, 17), 
(2, 3, 4)(5, 10, 19)(6, 15, 21)(7, 8, 20)(9, 12, 14)(11, 18, 16), 
(1, 9, 21)(2, 8, 12)(3, 15, 20)(4, 10, 19)(5, 14, 6)(11, 17, 16)
orbits: { 1, 21, 20, 14, 12, 15, 9, 7, 19, 8, 6, 11, 5, 10, 18, 17, 3, 16, 2, 4 }, { 13, 22 }

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
1 1 1 1 0 0 0 1 1 1 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 1 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
1 0 0 1 0 1 1 0 1 1 1 0 0 0 0 0 0 1 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
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 1 1 0 0 1 1 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 1
the automorphism group has order 11520
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 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 1 1 1 1 1 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 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 
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 
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 0 1 1 1 0 1 0 1 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 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 0 1 0 1 1 0 1 1 1 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 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 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 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 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 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 
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 
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 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 
, 
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 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 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 
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 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 
)
acting on the columns of the generator matrix as follows (in order):
(13, 22), 
(6, 14, 7)(8, 19, 16)(9, 21, 17)(10, 20, 11)(12, 18, 15), 
(5, 8, 16)(6, 9, 11)(7, 10, 18)(12, 20, 21)(14, 15, 17), 
(5, 7)(6, 14)(8, 15)(9, 10)(11, 16)(12, 20)(17, 18)(19, 21), 
(3, 4)(5, 8)(6, 9)(7, 15)(10, 14)(12, 20)(17, 18), 
(2, 4, 3)(5, 18, 15)(6, 11, 9)(7, 17, 8)(10, 14, 16), 
(1, 16)(2, 11)(3, 18)(4, 17)(5, 9)(6, 8)(7, 15)(10, 14)
orbits: { 1, 16, 19, 8, 11, 14, 21, 5, 15, 17, 6, 20, 9, 2, 10, 7, 18, 4, 12, 3 }, { 13, 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
1 1 1 1 0 0 0 1 1 1 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 1 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
1 0 0 1 0 1 1 0 1 1 1 0 0 0 0 0 0 1 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
1 1 0 0 0 1 1 1 0 1 0 1 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 1 0
0 1 1 0 1 1 0 1 0 1 0 0 1 0 0 0 0 0 0 0 0 1
the automorphism group has order 1152
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 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 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 
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 
1 0 1 0 0 1 1 1 1 0 0 0 1 
1 1 0 0 0 1 1 1 0 1 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 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 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 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 1 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 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 
, 
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), 
(5, 11)(6, 16)(7, 17)(12, 21)(13, 20)(14, 18)(19, 22), 
(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, 6)(3, 16)(4, 9)(7, 11)(8, 14)(10, 18)(12, 19), 
(1, 2, 6, 5)(3, 9, 14, 11)(4, 16, 7, 8)(10, 15, 18, 17)(12, 19)
orbits: { 1, 6, 5, 9, 16, 17, 2, 8, 11, 3, 18, 4, 10, 7, 15, 14 }, { 12, 13, 22, 21, 19, 20 }

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
1 1 1 1 0 0 0 1 1 1 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 1 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
1 0 0 1 0 1 1 0 1 1 1 0 0 0 0 0 0 1 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
1 1 0 0 0 1 1 1 0 1 0 1 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 1 0
0 0 0 1 1 1 1 1 0 0 1 1 1 0 0 0 0 0 0 0 0 1
the automorphism group has order 576
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 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 
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 0 1 1 0 1 1 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 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 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 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 
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 
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 
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 
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 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 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 
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 0 1 0 0 0 0 0 0 0 
1 0 0 0 0 0 0 0 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 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 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 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 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 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 1 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 
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 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 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 1 0 
0 0 0 0 0 0 0 0 0 0 0 0 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 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 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 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):
(5, 6)(7, 14)(8, 15)(9, 10)(11, 17)(13, 21)(16, 18), 
(3, 4)(5, 6)(8, 17)(9, 18)(10, 16)(11, 15)(12, 19), 
(2, 6, 5)(3, 17, 11)(4, 15, 8)(7, 18, 9)(10, 16, 14), 
(2, 3)(5, 17)(6, 11)(7, 18)(8, 15)(12, 20)(14, 16), 
(1, 2, 6)(3, 16, 15)(4, 9, 17)(7, 8, 10)(11, 18, 14), 
(1, 2, 5)(3, 18, 8)(4, 10, 11)(7, 17, 16)(9, 14, 15), 
(1, 14)(2, 7)(3, 6)(4, 5)(8, 18)(9, 17)(10, 16)(11, 15)
orbits: { 1, 6, 5, 14, 2, 11, 3, 17, 4, 7, 16, 18, 9, 15, 10, 8 }, { 12, 19, 20 }, { 13, 21 }, { 22 }

code no       9:
================
1 1 1 1 1 1 1 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 1 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
1 0 1 0 1 0 1 1 0 1 1 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 1 0 0 0 0
1 1 0 0 0 1 1 1 0 1 0 1 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 1 0 0
0 1 1 0 1 1 0 1 0 1 0 0 1 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 1
the automorphism group has order 432
and is strongly generated by the following 4 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 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 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 
1 0 1 0 0 1 1 1 1 0 0 0 1 
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 0 0 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 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 
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 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 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 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 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 1 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 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 1 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 1 0 0 0 0 0 0 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 
1 0 1 0 0 1 1 1 1 0 0 0 1 
)
acting on the columns of the generator matrix as follows (in order):
(5, 6, 7)(8, 10, 9)(11, 19, 20)(12, 21, 16)(13, 17, 18), 
(5, 10)(6, 8)(7, 9)(11, 19)(12, 16)(14, 15)(17, 18), 
(2, 5, 10)(3, 8, 6)(4, 11, 19)(12, 14, 17)(15, 16, 18), 
(1, 3, 9, 8, 7, 6)(2, 5, 10)(4, 18, 15, 12, 14, 19)(11, 17, 16)(13, 20)
orbits: { 1, 6, 5, 8, 7, 10, 2, 9, 3 }, { 4, 19, 11, 14, 20, 16, 15, 12, 13, 21, 17, 18 }, { 22 }