the 1 isometry classes of irreducible [24,14,6]_2 codes are:

code no       1:
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1 1 1 1 1 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 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
1 1 0 1 0 1 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
1 0 1 0 1 0 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
1 0 1 1 0 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
0 1 1 0 1 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
1 1 1 0 1 1 0 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
0 1 1 1 0 1 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0
1 1 0 0 1 0 1 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0
1 0 1 1 0 1 1 1 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0
1 0 1 1 1 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0
0 1 0 0 1 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0
1 0 0 0 0 1 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0
1 1 0 1 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 96
and is strongly generated by the following 3 elements:
(
1 0 0 0 0 0 0 0 0 0 
0 1 1 0 1 0 1 0 1 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 1 0 0 0 
0 0 0 0 0 1 0 0 0 0 
0 1 0 0 1 0 0 1 1 1 
0 0 0 0 1 0 0 0 0 0 
1 0 1 1 0 1 0 0 1 0 
1 1 0 1 0 1 0 1 0 0 
, 
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 1 0 0 0 
0 1 0 0 1 0 0 1 1 1 
1 0 1 1 0 1 1 1 0 1 
1 0 1 1 1 0 1 0 1 1 
0 0 0 0 0 0 0 0 0 1 
1 1 1 0 0 1 1 0 0 0 
0 0 0 0 0 0 0 1 0 0 
1 0 0 0 0 1 0 1 1 1 
, 
0 0 1 0 0 0 0 0 0 0 
1 1 0 1 0 0 1 1 1 1 
1 1 0 1 0 1 0 1 0 0 
1 0 1 0 1 0 1 1 0 0 
1 0 0 0 0 1 0 1 1 1 
1 1 1 0 0 1 1 0 0 0 
0 1 1 1 0 1 0 0 0 1 
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 1 0 0 0 
)
acting on the columns of the generator matrix as follows (in order):
(2, 17, 23, 16)(3, 15, 9, 4)(5, 8, 22, 7)(10, 20, 12, 13)(14, 18, 19, 24), 
(1, 21, 6, 11)(2, 12, 8, 9)(3, 23, 10, 7)(4, 17, 13, 22)(5, 15, 16, 20), 
(1, 23, 5, 11, 15, 12, 6, 8, 17, 21, 13, 3)(2, 9, 14, 4, 22, 18, 7, 10, 19, 20, 16, 24)
orbits: { 1, 11, 3, 6, 5, 4, 7, 13, 21, 12, 20, 23, 9, 22, 14, 10, 18, 17, 2, 15, 16, 19, 8, 24 }