the 1 isometry classes of irreducible [31,28,3]_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 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 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 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 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 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 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 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 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
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 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 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 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
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 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 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 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 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
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 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 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 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 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
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 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 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 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 0
4 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 0 4
the automorphism group has order 372000
and is strongly generated by the following 9 elements:
(
4 0 0 
0 2 0 
0 0 1 
, 
3 0 0 
0 1 0 
0 0 4 
, 
2 0 0 
0 1 0 
1 0 1 
, 
2 0 0 
0 1 0 
0 4 2 
, 
3 0 0 
0 4 2 
0 1 0 
, 
3 0 0 
4 4 2 
3 0 1 
, 
0 2 3 
2 2 4 
1 3 3 
, 
4 4 0 
4 2 3 
2 0 4 
, 
3 3 2 
4 1 2 
1 2 4 
)
acting on the columns of the generator matrix as follows (in order):
(4, 26, 28, 21)(5, 7, 8, 6)(9, 12)(10, 11)(13, 22, 27, 17)(14, 25, 29, 20)(15, 24, 30, 19)(16, 23, 31, 18), 
(4, 30, 16, 29)(5, 6, 8, 7)(9, 11, 12, 10)(13, 27)(14, 28, 15, 31)(17, 22)(18, 25, 21, 24)(19, 23, 20, 26), 
(3, 10, 11, 9)(4, 13, 14, 15)(5, 7, 8, 6)(17, 19, 20, 18)(22, 24, 25, 23)(27, 29, 30, 28), 
(3, 13, 22, 17)(4, 23, 18, 9)(5, 7, 8, 6)(10, 14, 24, 19)(11, 15, 25, 20)(12, 16, 26, 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), 
(2, 20, 8, 19)(3, 12, 10, 11)(4, 26, 13, 22)(5, 21, 7, 18)(6, 17)(14, 25, 16, 23)(15, 24)(27, 29, 30, 28), 
(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, 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), 
(1, 22, 13, 28, 24, 2, 11, 16, 10, 30, 23, 27, 26, 3, 19, 20, 29, 25, 17, 6, 8, 14, 15, 5, 18, 4, 21, 12, 9, 7, 31)
orbits: { 1, 27, 5, 31, 22, 13, 28, 25, 23, 6, 7, 21, 18, 15, 17, 20, 4, 3, 26, 12, 14, 30, 29, 19, 24, 11, 16, 9, 8, 10, 2 }