the 1 isometry classes of irreducible [29,24,3]_2 codes are:

code no       1:
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1 1 1 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 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 0
1 0 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
0 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 0
1 1 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 0
1 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 0 0
0 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 0
1 1 0 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
0 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
1 0 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 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 0 0
1 1 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 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 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
1 1 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 0 0
0 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
1 0 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 0
0 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 0
1 1 1 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 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
1 0 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 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 0 1 0 0
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 0 1 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 0 1
the automorphism group has order 21504
and is strongly generated by the following 10 elements:
(
1 0 0 0 0 
0 1 0 0 0 
0 0 1 0 0 
0 0 0 1 0 
1 1 0 0 1 
, 
1 0 0 0 0 
0 1 0 0 0 
0 0 1 0 0 
0 0 1 0 1 
0 0 1 1 0 
, 
1 0 0 0 0 
0 1 0 0 0 
0 0 1 0 0 
1 0 0 1 0 
1 0 0 0 1 
, 
1 0 0 0 0 
0 1 0 0 0 
0 0 1 0 0 
1 1 1 0 1 
1 1 1 1 0 
, 
1 0 0 0 0 
0 1 0 0 0 
0 0 1 0 0 
0 0 1 1 0 
0 0 1 0 1 
, 
1 0 0 0 0 
0 1 0 0 0 
1 1 1 0 0 
1 0 0 1 0 
0 1 0 0 1 
, 
1 0 0 0 0 
0 1 0 0 0 
0 1 1 0 0 
1 1 0 1 0 
1 0 0 0 1 
, 
1 0 0 0 0 
0 1 0 0 0 
1 1 0 0 1 
0 1 0 1 1 
1 0 1 0 1 
, 
0 1 0 0 0 
1 0 0 0 0 
0 0 1 0 0 
0 0 0 0 1 
0 0 0 1 0 
, 
1 1 0 1 1 
0 0 0 1 1 
0 0 1 1 1 
0 0 0 1 0 
0 1 0 0 1 
)
acting on the columns of the generator matrix as follows (in order):
(5, 20)(6, 29)(18, 19)(21, 24)(22, 23)(25, 28)(26, 27), 
(4, 21)(5, 14)(11, 22)(12, 23)(13, 24)(15, 18)(16, 19)(17, 20), 
(4, 11)(5, 18)(12, 13)(14, 15)(16, 17)(19, 20)(21, 22)(23, 24), 
(4, 24)(5, 17)(11, 23)(12, 22)(13, 21)(14, 20)(15, 19)(16, 18), 
(4, 14)(5, 21)(11, 15)(12, 16)(13, 17)(18, 22)(19, 23)(20, 24), 
(3, 10)(4, 11)(5, 19)(8, 9)(12, 13)(14, 16)(15, 17)(18, 20)(21, 22)(23, 24)(25, 28)(26, 27), 
(3, 9)(4, 13)(5, 18)(8, 10)(11, 12)(14, 15)(16, 17)(19, 20)(21, 24)(22, 23)(25, 27)(26, 28), 
(3, 23, 20)(4, 15, 27)(5, 10, 22)(8, 24, 19)(9, 21, 18)(11, 14, 28)(12, 17, 25)(13, 16, 26), 
(1, 2)(4, 5)(8, 9)(11, 19)(12, 18)(13, 20)(14, 21)(15, 23)(16, 22)(17, 24)(26, 27), 
(1, 26, 28)(2, 27, 25)(3, 9, 29)(5, 12, 19)(6, 10, 8)(11, 18, 20)(14, 16, 21)(15, 24, 17)
orbits: { 1, 2, 28, 25, 26, 14, 27, 17, 16, 5, 15, 20, 4, 11, 21, 13, 12, 24, 19, 18, 22, 23, 9, 8, 10, 3, 6, 29 }, { 7 }