the 1 isometry classes of irreducible [29,26,3]_5 codes are:

code no       1:
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1 1 1 4 0 0 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 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 1 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
3 1 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
4 1 0 0 0 0 0 4 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 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 0 1 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
3 0 1 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
4 0 1 0 0 0 0 0 0 0 0 4 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 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 1 1 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
3 1 1 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0
4 1 1 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0
0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0
1 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0
2 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0
3 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0
4 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0
0 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0
1 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0
2 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0
3 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0
4 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0
0 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0
1 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0
2 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4
the automorphism group has order 800
and is strongly generated by the following 6 elements:
(
2 0 0 
0 1 0 
0 4 2 
, 
2 0 0 
0 2 0 
1 4 3 
, 
1 0 0 
1 3 1 
1 2 2 
, 
3 0 0 
0 4 2 
0 1 0 
, 
2 3 2 
1 0 3 
1 2 1 
, 
4 3 2 
4 0 1 
0 0 1 
)
acting on the columns of the generator matrix as follows (in order):
(3, 13, 22, 17)(4, 23, 18, 9)(5, 7, 8, 6)(10, 14, 24, 19)(11, 15, 25, 20)(12, 16, 26, 21), 
(3, 24)(4, 18)(9, 23)(10, 22)(11, 26)(12, 25)(13, 19)(14, 17)(15, 21)(16, 20)(27, 29), 
(2, 23)(3, 15)(4, 9)(5, 24)(6, 25)(7, 26)(8, 22)(10, 16)(11, 14)(12, 13)(17, 19)(20, 21), 
(2, 3, 13, 17)(4, 20, 6, 12)(5, 10, 15, 21)(7, 9, 16, 19)(8, 11, 14, 18)(23, 24, 26, 25), 
(1, 28)(2, 10)(3, 18)(4, 12)(6, 22)(7, 15)(8, 21)(11, 23)(13, 25)(16, 17)(19, 24), 
(1, 27, 28, 29)(2, 16, 26, 12)(4, 5, 25, 19)(7, 10, 13, 20)(8, 18, 11, 22)(9, 17, 24, 15)
orbits: { 1, 28, 29, 27 }, { 2, 23, 17, 10, 12, 4, 9, 25, 11, 22, 14, 19, 13, 16, 5, 7, 21, 6, 26, 18, 15, 20, 8, 24, 3 }