the 1 isometry classes of irreducible [31,26,3]_2 codes are:

code no       1:
================
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 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 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 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 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 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 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 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
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 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 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 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 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 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 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
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 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 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 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 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
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 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 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
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 0 0
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 0 1 0
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 0 1
the automorphism group has order 9999360
and is strongly generated by the following 15 elements:
(
1 0 0 0 0 
0 1 0 0 0 
0 0 1 0 0 
0 0 0 1 0 
0 0 1 1 1 
, 
1 0 0 0 0 
0 1 0 0 0 
0 0 1 0 0 
0 0 0 1 0 
0 1 1 0 1 
, 
1 0 0 0 0 
0 1 0 0 0 
0 0 1 0 0 
0 0 0 1 0 
0 0 1 0 1 
, 
1 0 0 0 0 
0 1 0 0 0 
0 0 1 0 0 
0 0 0 1 0 
1 1 1 1 1 
, 
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 
0 1 0 0 1 
0 1 0 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 
0 0 1 0 0 
0 1 0 1 0 
0 1 0 0 1 
, 
1 0 0 0 0 
0 1 0 0 0 
0 0 1 0 0 
0 1 0 1 1 
1 1 1 1 0 
, 
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 
, 
1 0 0 0 0 
1 0 0 1 0 
1 0 0 0 1 
1 1 0 0 0 
1 0 1 0 0 
, 
1 0 0 0 0 
0 1 0 1 0 
0 0 1 0 0 
0 0 0 1 0 
0 0 0 1 1 
, 
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 
, 
0 1 0 0 0 
1 0 0 0 0 
0 0 1 0 0 
0 0 0 0 1 
1 1 0 1 0 
, 
0 1 1 1 1 
0 1 1 0 1 
1 0 0 0 0 
0 0 1 1 0 
0 1 1 1 0 
)
acting on the columns of the generator matrix as follows (in order):
(5, 29)(6, 20)(18, 30)(19, 31)(21, 25)(22, 26)(23, 27)(24, 28), 
(5, 23)(6, 26)(18, 24)(19, 21)(20, 22)(25, 31)(27, 29)(28, 30), 
(5, 21)(6, 28)(18, 22)(19, 23)(20, 24)(25, 29)(26, 30)(27, 31), 
(5, 6)(18, 31)(19, 30)(20, 29)(21, 28)(22, 27)(23, 26)(24, 25), 
(4, 11)(5, 18)(12, 13)(14, 15)(16, 17)(19, 20)(21, 22)(23, 24), 
(4, 19)(5, 12)(11, 20)(13, 18)(14, 23)(15, 24)(16, 21)(17, 22), 
(4, 14)(5, 21)(11, 15)(12, 16)(13, 17)(18, 22)(19, 23)(20, 24), 
(4, 12)(5, 19)(11, 13)(14, 16)(15, 17)(18, 20)(21, 23)(22, 24), 
(4, 24, 27)(5, 30, 17)(6, 15, 19)(11, 23, 28)(12, 22, 25)(13, 21, 26)(14, 20, 31)(16, 18, 29), 
(3, 23, 20)(4, 15, 27)(5, 10, 22)(8, 24, 19)(9, 21, 18)(11, 14, 28)(12, 17, 25)(13, 16, 26), 
(2, 11)(3, 18)(4, 7)(5, 8)(9, 25)(10, 26)(14, 19)(15, 20)(16, 28)(17, 27)(23, 30)(24, 29), 
(2, 12)(5, 25)(7, 13)(9, 16)(10, 17)(18, 26)(21, 29)(22, 30), 
(1, 26, 28)(2, 27, 25)(3, 9, 29)(5, 12, 19)(6, 10, 8)(11, 18, 20)(14, 16, 21)(15, 24, 17), 
(1, 2)(4, 20, 13, 5)(6, 29)(8, 9)(11, 18, 12, 19)(14, 24, 17, 21)(15, 22, 16, 23)(25, 28), 
(1, 3, 13, 6, 8, 17, 21, 27, 12, 28, 16, 5, 18, 22, 31)(2, 25, 19, 11, 10, 24, 9, 20, 15, 14, 4, 7, 29, 26, 23)
orbits: { 1, 28, 2, 31, 24, 30, 6, 21, 23, 14, 16, 26, 25, 12, 11, 19, 27, 18, 20, 22, 15, 4, 8, 29, 10, 5, 13, 9, 17, 3, 7 }