the 1 isometry classes of irreducible [29,23,4]_2 codes are:

code no       1:
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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 0 0 0 0
1 1 0 1 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 0 1 1 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 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 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 0 0
1 0 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
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 0 0
1 0 0 1 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 1 0 1 1 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 1 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
1 1 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 0
1 1 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 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 1 1 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 1 0 1 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 1 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
0 0 1 1 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
1 1 1 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
1 0 0 0 1 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 1 0 0 1 1 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 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
1 1 1 0 1 1 0 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 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
the automorphism group has order 64512
and is strongly generated by the following 11 elements:
(
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
0 0 0 1 0 0 
1 0 1 0 1 0 
1 0 1 0 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
0 0 0 1 0 0 
0 0 1 1 0 1 
0 0 1 1 1 0 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
0 0 0 1 0 0 
0 1 1 0 0 1 
0 1 1 0 1 0 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
0 0 0 1 0 0 
1 1 0 0 1 0 
1 1 0 0 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
1 0 1 1 0 0 
1 0 0 1 1 0 
0 0 1 1 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
0 1 1 1 0 0 
0 1 0 1 1 0 
0 0 1 1 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
1 0 0 1 1 0 
1 1 1 0 1 1 
0 1 1 0 1 0 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
1 1 1 0 0 0 
1 1 0 1 0 0 
0 1 0 1 0 1 
1 0 0 1 1 0 
, 
1 0 0 0 0 0 
1 1 1 0 0 0 
0 0 1 0 0 0 
1 1 0 1 0 0 
0 0 1 1 1 0 
1 1 1 1 0 1 
, 
0 1 0 1 1 0 
1 0 0 1 1 0 
1 1 1 1 1 0 
1 1 0 0 1 0 
1 0 0 0 0 0 
0 1 0 1 0 1 
, 
1 1 1 0 1 1 
0 1 0 0 1 1 
1 0 0 0 1 1 
1 1 1 0 0 0 
1 1 1 1 0 1 
0 0 0 0 1 0 
)
acting on the columns of the generator matrix as follows (in order):
(5, 12)(6, 19)(11, 13)(14, 16)(15, 17)(18, 20)(21, 23)(22, 24), 
(5, 23)(6, 16)(11, 24)(12, 21)(13, 22)(14, 19)(15, 20)(17, 18), 
(5, 20)(6, 13)(11, 19)(12, 18)(14, 24)(15, 23)(16, 22)(17, 21), 
(5, 11)(6, 18)(12, 13)(14, 15)(16, 17)(19, 20)(21, 22)(23, 24), 
(4, 9)(5, 16, 12, 14)(6, 21, 19, 23)(8, 10)(11, 17, 13, 15)(18, 22, 20, 24)(25, 27)(26, 28), 
(4, 10)(5, 16, 13, 15)(6, 22, 20, 23)(8, 9)(11, 17, 12, 14)(18, 21, 19, 24)(25, 28)(26, 27), 
(4, 24, 14)(5, 20, 28)(6, 25, 13)(8, 23, 15)(9, 22, 16)(10, 21, 17)(11, 19, 27)(12, 18, 26), 
(3, 7)(4, 8)(5, 22)(6, 14)(11, 21)(12, 23)(13, 24)(15, 18)(16, 20)(17, 19)(25, 26), 
(2, 7)(4, 10, 9, 8)(5, 15, 11, 16)(6, 23, 20, 24)(12, 17, 13, 14)(18, 22, 19, 21)(25, 28, 27, 26), 
(1, 5, 8, 15)(2, 11, 4, 14)(3, 12, 10, 17)(6, 22)(7, 13, 9, 16)(18, 21)(19, 24)(20, 23), 
(1, 9, 26, 2, 8, 28)(3, 10, 27, 7, 4, 25)(5, 6, 21, 12, 18, 24)(11, 20, 23, 13, 19, 22)(14, 16, 17)
orbits: { 1, 15, 28, 17, 20, 23, 14, 13, 18, 5, 8, 26, 25, 21, 16, 11, 19, 12, 10, 22, 24, 6, 4, 7, 9, 2, 27, 3 }, { 29 }