the 1 isometry classes of irreducible [23,11,8]_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
1 1 1 1 0 0 0 1 1 1 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 1 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
1 0 0 1 0 1 1 0 1 1 1 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 1 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 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 1 1 1 1 1 0 0 1 1 0 0 0 0 0 0 0 0 1 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 1 1 1 0 0 1 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 1
the automorphism group has order 10200960
and is strongly generated by the following 12 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 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 1 0 
1 0 0 1 0 1 1 0 1 1 1 0 
1 1 0 0 1 1 0 1 1 0 1 0 
0 1 0 1 1 1 0 0 1 1 0 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 0 0 0 0 0 0 1 0 
1 0 0 1 0 1 1 0 1 1 1 0 
1 1 0 0 1 1 0 1 1 0 1 0 
0 1 0 1 1 1 0 0 1 1 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 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 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 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 
1 0 0 1 0 1 1 0 1 1 1 0 
1 1 0 0 1 1 0 1 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 1 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 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 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 
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 
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 1 0 1 1 1 0 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 
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 
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 0 0 0 0 1 0 0 0 0 0 0 
1 1 1 1 1 1 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 1 0 0 0 0 0 
1 1 0 0 0 1 1 1 0 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 
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 0 0 0 0 0 0 0 0 1 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 1 1 1 1 1 0 0 1 1 
1 1 1 1 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 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 0 0 
0 1 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 1 0 0 0 
1 0 1 1 1 0 0 0 1 0 1 1 
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 1 1 1 0 0 0 1 1 1 0 0 
0 0 0 1 1 1 1 1 0 0 1 1 
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 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 
)
acting on the columns of the generator matrix as follows (in order):
(6, 13, 7)(8, 20, 11)(9, 18, 17)(10, 12, 15)(14, 19, 16)(21, 23, 22), 
(5, 11)(6, 17)(7, 15)(8, 20)(9, 12)(10, 19)(13, 16)(14, 18), 
(5, 15)(6, 16)(7, 11)(8, 18)(9, 19)(10, 12)(13, 17)(14, 20), 
(5, 19)(6, 20)(7, 12)(8, 17)(9, 15)(10, 11)(13, 18)(14, 16), 
(5, 17)(6, 11)(7, 16)(8, 19)(9, 18)(10, 20)(12, 14)(13, 15), 
(4, 22, 21)(5, 19, 6)(7, 8, 15)(9, 18, 10)(11, 16, 12)(13, 17, 14), 
(4, 13, 23, 14)(5, 10)(6, 19, 18, 9)(7, 16, 11, 8)(12, 15)(17, 21, 20, 22), 
(3, 4, 22)(5, 18, 10)(6, 7, 11)(8, 20, 13)(9, 14, 15)(12, 17, 19), 
(3, 11, 5, 18, 14)(4, 10, 20, 7, 16)(6, 12, 15, 21, 8)(9, 22, 17, 19, 13), 
(2, 3, 14, 9, 5, 22, 6)(4, 7, 16, 13, 12, 11, 19)(8, 17, 18, 20, 21, 10, 15), 
(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)
orbits: { 1, 4, 23, 21, 14, 3, 16, 19, 9, 2, 13, 8, 22, 17, 15, 20, 18, 12, 5, 6, 7, 11, 10 }