the 1 isometry classes of irreducible [23,12,7]_2 codes are:

code no       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 1 1 1 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
1 1 1 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0
1 0 0 1 1 0 1 1 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0
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 1 0 1 1 0 1 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0
0 0 1 1 0 1 1 1 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0
1 0 0 0 1 1 1 0 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0
0 1 0 1 1 0 0 1 1 0 1 0 0 0 0 0 0 0 0 1 0 0 0
0 1 1 0 1 0 1 0 0 1 1 0 0 0 0 0 0 0 0 0 1 0 0
1 1 0 0 0 1 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 1 0
1 0 1 1 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1
the automorphism group has order 10200960
and is strongly generated by the following 13 elements:
(
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 0 0 0 1 0 
1 0 0 1 1 0 1 1 0 1 0 
0 1 0 1 0 1 1 0 1 1 0 
0 0 0 0 0 0 1 0 0 0 0 
0 1 1 0 1 0 1 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 0 0 0 0 1 0 0 0 0 0 
1 0 0 1 1 0 1 1 0 1 0 
0 0 0 0 0 0 0 0 0 1 0 
0 0 1 0 1 1 0 1 1 1 0 
0 0 0 0 0 0 0 1 0 0 0 
1 1 0 0 0 1 0 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 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 
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 1 0 0 0 
0 0 1 0 1 1 0 1 1 1 0 
0 1 0 1 1 0 0 1 1 0 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 0 0 0 0 1 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 1 
0 0 1 1 0 1 1 1 0 0 1 
1 0 0 0 1 1 1 0 1 0 1 
0 1 1 0 1 0 1 0 0 1 1 
0 0 0 0 0 0 1 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 0 0 0 0 0 
0 0 0 0 1 0 0 0 0 0 0 
0 1 0 1 1 0 0 1 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 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 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 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 1 0 0 0 0 
1 1 1 0 0 0 1 1 1 0 0 
0 1 0 1 0 1 1 0 1 1 0 
0 1 0 1 1 0 0 1 1 0 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 1 0 1 0 1 1 0 1 1 0 
1 0 0 1 1 0 1 1 0 1 0 
0 0 1 0 1 1 0 1 1 1 0 
1 0 0 0 1 1 1 0 1 0 1 
0 0 1 1 0 1 1 1 0 0 1 
0 1 0 1 1 0 0 1 1 0 1 
1 1 1 1 1 1 0 0 0 0 0 
1 1 1 0 0 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 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 1 1 0 1 1 1 0 0 1 
1 0 0 0 1 1 1 0 1 0 1 
0 0 1 0 1 1 0 1 1 1 0 
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 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 1 0 0 0 0 0 0 0 0 0 
0 1 1 0 1 0 1 0 0 1 1 
0 0 1 1 0 1 1 1 0 0 1 
0 0 0 0 0 0 1 0 0 0 0 
1 0 0 1 1 0 1 1 0 1 0 
0 1 0 1 1 0 0 1 1 0 1 
0 0 0 1 0 0 0 0 0 0 0 
1 1 1 0 0 0 1 1 1 0 0 
0 0 0 0 0 0 0 0 1 0 0 
1 0 0 0 1 1 1 0 1 0 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 0 1 0 
0 0 1 1 0 1 1 1 0 0 1 
0 0 0 0 1 0 0 0 0 0 0 
1 1 1 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 0 1 0 0 0 
1 1 0 0 0 1 0 1 0 1 1 
0 1 0 1 1 0 0 1 1 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 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 1 0 0 0 0 
1 0 0 1 1 0 1 1 0 1 0 
0 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 1 0 1 0 1 1 0 1 1 0 
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 1 0 0 0 0 
1 0 0 1 1 0 1 1 0 1 0 
0 0 1 1 0 1 1 1 0 0 1 
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 0 1 1 1 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 1 0 0 0 0 0 0 0 
, 
1 0 1 1 0 0 0 0 1 1 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 0 0 1 0 1 0 1 1 
0 0 1 1 0 1 1 1 0 0 1 
0 1 1 0 1 0 1 0 0 1 1 
1 1 1 0 0 0 1 1 1 0 0 
0 0 0 0 1 0 0 0 0 0 0 
1 0 0 0 1 1 1 0 1 0 1 
1 1 1 1 1 1 1 1 1 1 1 
0 0 0 0 0 0 0 0 1 0 0 
)
acting on the columns of the generator matrix as follows (in order):
(7, 10)(8, 15)(9, 16)(11, 21)(12, 20)(14, 17)(18, 22)(19, 23), 
(7, 15)(8, 10)(9, 17)(11, 22)(12, 19)(14, 16)(18, 21)(20, 23), 
(7, 14)(8, 9)(10, 17)(11, 20)(12, 21)(15, 16)(18, 19)(22, 23), 
(7, 11)(8, 18)(9, 19)(10, 21)(12, 17)(14, 20)(15, 22)(16, 23), 
(5, 6, 13)(7, 15, 20)(8, 16, 18)(9, 10, 11)(12, 22, 21)(14, 17, 19), 
(4, 13)(5, 6)(7, 8)(9, 14)(10, 16)(11, 20)(15, 17)(18, 19), 
(4, 16)(5, 15)(6, 17)(7, 19)(8, 18)(9, 20)(10, 13)(11, 14), 
(4, 11)(5, 18)(6, 19)(7, 17)(8, 15)(9, 10)(13, 20)(14, 16), 
(3, 12, 21)(4, 8, 18)(5, 20, 7)(6, 13, 15)(9, 10, 14)(11, 17, 19), 
(3, 20, 10)(4, 16, 18)(6, 7, 12)(9, 13, 22)(11, 14, 15)(17, 19, 21), 
(2, 19, 20, 14, 8)(3, 17, 18, 7, 5)(4, 13, 12, 16, 10)(6, 9, 21, 11, 15), 
(1, 18, 4, 11, 5)(2, 17, 16, 14, 7)(3, 8, 20, 13, 15)(6, 9, 10, 19, 12), 
(1, 19, 9, 11, 22, 4, 16, 15, 12, 10, 23)(2, 18, 5, 8, 13, 14, 7, 21, 6, 3, 17)
orbits: { 1, 5, 23, 13, 6, 15, 18, 7, 11, 19, 20, 22, 16, 10, 4, 9, 8, 17, 12, 21, 14, 2, 3 }