the 1 isometry classes of irreducible [23,14,5]_2 codes are:

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