the 1 isometry classes of irreducible [24,12,8]_2 codes are:

code no       1:
================
1 1 1 1 1 1 1 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 0 0 0 0 0 0 0 0 0
1 1 0 0 1 1 0 1 1 0 1 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 1 0 0 0 0 0 0 0 0
1 0 0 1 0 1 1 0 1 1 1 0 0 0 0 0 1 0 0 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 0 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 1 0 1 1 1 0 0 1 1 0 1 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 0 0 0 0 1 0 0 0
1 0 1 1 1 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 1 0 0
0 1 1 1 0 0 1 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 1 0
0 0 1 0 0 1 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1
the automorphism group has order 244823040
and is strongly generated by the following 16 elements:
(
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 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 
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 1 0 0 0 
1 0 0 1 0 1 1 0 1 1 1 0 
0 1 0 1 1 1 0 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 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 1 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 
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 1 1 1 1 1 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 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 1 0 0 0 0 0 
1 1 0 0 0 1 1 1 0 1 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 1 
0 1 1 1 0 0 1 0 0 1 1 1 
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 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 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 1 
0 1 1 0 1 0 1 1 1 0 0 1 
1 1 0 0 0 1 1 1 0 1 0 1 
0 0 0 1 1 1 1 1 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 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 
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 1 0 1 1 1 0 0 1 1 0 1 
0 1 1 0 1 0 1 1 1 0 0 1 
0 0 0 0 0 0 0 0 0 0 0 1 
0 0 0 0 0 0 0 1 0 0 0 0 
1 1 0 0 1 1 0 1 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 1 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 
1 0 1 0 1 0 1 1 0 1 1 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 
1 1 0 0 0 1 1 1 0 1 0 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 0 0 0 0 0 0 1 0 0 
, 
1 0 0 0 0 0 0 0 0 0 0 0 
0 1 0 0 0 0 0 0 0 0 0 0 
0 0 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 1 0 1 1 0 1 1 1 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 
1 1 0 0 0 1 1 1 0 1 0 1 
0 1 1 0 1 0 1 1 1 0 0 1 
0 1 0 1 1 1 0 0 1 1 0 1 
0 0 0 0 0 1 0 0 0 0 0 0 
1 1 1 1 0 0 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 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 
1 1 1 1 0 0 0 1 1 1 0 0 
0 0 0 0 0 0 0 1 0 0 0 0 
1 0 0 1 0 1 1 0 1 1 1 0 
1 0 1 0 1 0 1 1 0 1 1 0 
1 1 0 0 1 1 0 1 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 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 1 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 1 0 0 0 0 0 0 
1 1 0 0 0 1 1 1 0 1 0 1 
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 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 1 
1 0 1 0 1 0 1 1 0 1 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 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 1 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 1 1 0 1 0 1 1 1 0 0 1 
0 0 0 1 0 0 0 0 0 0 0 0 
1 1 0 0 0 1 1 1 0 1 0 1 
1 0 1 1 1 0 0 0 1 0 1 1 
0 0 0 0 0 0 0 0 1 0 0 0 
, 
1 0 0 0 0 0 0 0 0 0 0 0 
0 1 0 0 0 0 0 0 0 0 0 0 
0 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 1 0 
1 0 1 1 1 0 0 0 1 0 1 1 
0 1 1 1 0 0 1 0 0 1 1 1 
0 0 0 0 0 0 0 1 0 0 0 0 
0 1 1 0 1 0 1 1 1 0 0 1 
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 1 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 1 1 1 1 1 0 0 1 1 
1 1 1 1 1 1 1 0 0 0 0 0 
0 1 0 1 1 1 0 0 1 1 0 1 
1 0 1 1 1 0 0 0 1 0 1 1 
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 1 1 0 1 0 1 1 1 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 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 1 1 1 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 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 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 1 1 1 1 0 0 1 1 
1 0 1 1 1 0 0 0 1 0 1 1 
1 1 1 1 0 0 0 1 1 1 0 0 
, 
0 0 0 1 0 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 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 0 
1 0 0 1 0 1 1 0 1 1 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 1 
1 1 0 0 0 1 1 1 0 1 0 1 
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 1 1 1 0 0 1 0 0 1 1 1 
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 1 0 0 0 0 0 0 0 0 0 0 
1 1 0 0 1 1 0 1 1 0 1 0 
1 1 1 1 1 1 1 0 0 0 0 0 
1 0 1 1 1 0 0 0 1 0 1 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 0 1 0 
0 1 1 0 1 0 1 1 1 0 0 1 
1 0 0 0 0 0 0 0 0 0 0 0 
, 
0 0 1 0 0 1 0 1 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 0 1 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 
1 0 1 1 1 0 0 0 1 0 1 1 
0 1 1 1 0 0 1 0 0 1 1 1 
0 1 0 1 1 1 0 0 1 1 0 1 
1 1 1 1 0 0 0 1 1 1 0 0 
1 0 1 0 1 0 1 1 0 1 1 0 
0 0 1 0 0 0 0 0 0 0 0 0 
0 0 0 0 1 0 0 0 0 0 0 0 
)
acting on the columns of the generator matrix as follows (in order):
(8, 14)(9, 10)(11, 17)(12, 20)(15, 16)(18, 19)(21, 24)(22, 23), 
(8, 11)(9, 15)(10, 16)(12, 21)(14, 17)(18, 22)(19, 23)(20, 24), 
(8, 19)(9, 20)(10, 12)(11, 23)(14, 18)(15, 24)(16, 21)(17, 22), 
(8, 12)(9, 18)(10, 19)(11, 21)(14, 20)(15, 22)(16, 23)(17, 24), 
(6, 7, 13)(8, 11, 20)(9, 17, 18)(10, 15, 12)(14, 16, 19)(21, 22, 23), 
(5, 15)(6, 16)(7, 11)(8, 18)(9, 19)(10, 12)(13, 17)(14, 20), 
(5, 17)(6, 11)(7, 16)(8, 19)(9, 18)(10, 20)(12, 14)(13, 15), 
(5, 15, 10)(6, 11, 14)(7, 17, 8)(9, 13, 16)(18, 19, 20)(21, 22, 23), 
(4, 22, 21)(5, 19, 6)(7, 8, 15)(9, 18, 10)(11, 16, 12)(13, 17, 14), 
(4, 9, 12)(5, 22, 11)(6, 18, 8)(7, 15, 21)(10, 23, 19)(14, 17, 20), 
(3, 22, 6, 12)(4, 15)(5, 23, 7, 11)(9, 16, 20, 18)(10, 21, 17, 14)(13, 19), 
(2, 13, 4, 19)(3, 12, 14, 21)(5, 16, 17, 20)(6, 11, 23, 22)(8, 15)(9, 18), 
(2, 7, 19, 20, 18, 17, 24)(3, 13, 23, 14, 12, 4, 15)(5, 6, 9, 22, 11, 21, 10), 
(1, 12, 9, 4)(2, 17, 7, 16)(3, 5)(6, 13, 18, 8)(10, 19)(14, 15, 20, 21), 
(1, 12, 14, 20, 16, 13, 6, 22, 7, 2, 4, 3, 8, 23)(5, 15)(9, 21, 17, 19, 18, 11, 10), 
(1, 16, 10, 15, 14, 9, 19, 18, 17, 24)(2, 21, 23, 7, 22, 6, 20, 8, 13, 4)(3, 11)(5, 12)
orbits: { 1, 4, 23, 24, 21, 12, 15, 13, 9, 2, 22, 19, 11, 16, 10, 5, 8, 20, 17, 14, 6, 3, 7, 18 }