the 1 isometry classes of irreducible [31,25,4]_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 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 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 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 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 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 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 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 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
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 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 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 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 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 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 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
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 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 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 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
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 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 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 0 0
1 1 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 0
1 0 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 0 1
the automorphism group has order 9999360
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 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 
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 0 0 0 1 
0 0 0 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 
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 1 1 0 1 
0 0 0 1 0 0 
0 0 1 1 1 0 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
1 0 1 1 0 0 
0 1 0 1 1 0 
1 1 1 1 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 1 1 0 1 0 
0 0 1 0 0 0 
0 1 0 0 1 1 
0 0 1 1 1 0 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 1 0 1 0 1 
0 1 0 0 1 1 
1 1 1 0 1 1 
1 1 0 0 1 0 
, 
1 0 0 0 0 0 
0 1 1 1 0 0 
0 0 0 0 1 0 
0 0 0 1 1 1 
1 1 0 0 1 0 
1 1 0 1 0 0 
, 
1 1 1 0 0 0 
0 0 1 0 0 0 
0 1 0 0 0 0 
0 0 1 0 1 1 
0 0 0 0 1 0 
0 0 1 1 1 0 
, 
1 0 1 1 1 1 
0 1 0 0 1 1 
1 1 1 1 1 0 
0 1 1 0 1 0 
1 1 1 0 0 0 
0 1 0 0 0 0 
)
acting on the columns of the generator matrix as follows (in order):
(5, 11)(6, 18)(12, 13)(14, 15)(16, 17)(19, 20)(21, 22)(23, 24), 
(5, 12)(6, 19)(11, 13)(14, 16)(15, 17)(18, 20)(21, 23)(22, 24), 
(5, 6)(11, 18)(12, 19)(13, 20)(14, 21)(15, 22)(16, 23)(17, 24), 
(5, 23)(6, 16)(11, 24)(12, 21)(13, 22)(14, 19)(15, 20)(17, 18), 
(4, 5, 27, 23)(6, 16)(8, 11, 28, 24)(9, 12, 25, 21)(10, 13, 26, 22)(14, 19)(15, 20)(17, 18), 
(4, 9)(5, 17, 12, 15)(6, 22, 19, 24)(8, 10)(11, 16, 13, 14)(18, 21, 20, 23)(25, 27)(26, 28), 
(3, 4, 20, 13)(5, 10, 23, 26)(6, 16)(7, 8, 19, 12)(9, 24, 25, 11)(14, 21, 30, 28)(15, 22, 29, 27)(17, 18), 
(3, 14, 9, 28, 5, 18, 22)(4, 24, 16, 12, 30, 20, 26)(6, 21, 7, 15, 10, 27, 11)(8, 23, 17, 13, 29, 19, 25), 
(2, 12, 20, 10)(3, 18, 23, 24, 30, 16, 11, 5)(4, 27, 17, 7, 28, 8, 6, 29)(9, 13, 26, 21)(14, 25, 31, 22)(15, 19), 
(1, 7)(2, 3)(4, 26, 10, 27)(6, 15, 20, 16)(8, 25, 9, 28)(14, 19, 17, 18)(21, 24)(22, 23), 
(1, 17, 3, 24, 20, 22, 13, 4, 11, 29, 25, 31)(2, 6, 19, 12, 28, 26)(5, 7)(8, 23, 14)(9, 18, 15, 27)(10, 16, 30)
orbits: { 1, 7, 31, 12, 21, 17, 5, 25, 13, 19, 9, 16, 2, 22, 23, 14, 18, 6, 26, 24, 15, 27, 11, 4, 28, 8, 29, 20, 10, 30, 3 }