the 1 isometry classes of irreducible [30,27,3]_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 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 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 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 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 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 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 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 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
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 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 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 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
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 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 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 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 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
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 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 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 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 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
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 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 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 0
3 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 0 4
the automorphism group has order 12000
and is strongly generated by the following 8 elements:
(
2 0 0 
0 1 0 
0 4 2 
, 
4 0 0 
0 1 0 
2 4 2 
, 
1 0 0 
1 3 1 
1 2 2 
, 
3 0 0 
0 4 2 
0 1 0 
, 
4 1 4 
0 3 1 
2 2 2 
, 
0 2 3 
2 2 4 
1 3 3 
, 
4 2 3 
4 4 2 
4 2 4 
, 
4 4 0 
4 2 3 
2 0 4 
)
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, 14, 25, 18)(4, 22, 19, 11)(5, 8)(6, 7)(9, 13, 24, 20)(10, 15, 23, 17)(12, 16, 26, 21)(27, 29, 30, 28), 
(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, 6, 22)(3, 19, 25, 4)(7, 15, 8, 21)(9, 11, 26, 23)(12, 13, 24, 18)(14, 16, 20, 17)(27, 29), 
(1, 29, 28, 27)(2, 20, 11, 25)(3, 21, 23, 14)(4, 26, 10, 8)(5, 12, 13, 18)(7, 22, 19, 16), 
(1, 28, 29, 30)(2, 15, 13, 19)(3, 12, 17, 23)(4, 26, 24, 20)(5, 21, 9, 7)(6, 10, 25, 16)(8, 22)(11, 14), 
(1, 21, 15, 13, 8, 19, 28, 16, 9, 23, 11, 3, 30, 2, 17, 10, 14, 25, 27, 26, 24, 7, 18, 5)(4, 29, 12, 6, 20, 22)
orbits: { 1, 28, 27, 30, 5, 29, 19, 25, 3, 6, 8, 24, 21, 18, 7, 4, 22, 17, 16, 13, 15, 14, 26, 11, 10, 2, 23, 20, 12, 9 }