the 1 isometry classes of irreducible [21,10,7]_2 codes are:

code no       1:
================
1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0
1 1 1 1 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
1 1 1 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 0 0 0
1 0 0 1 1 0 1 1 0 1 0 0 0 0 1 0 0 0 0 0 0
0 1 0 1 0 1 1 0 1 1 0 0 0 0 0 1 0 0 0 0 0
0 0 1 0 1 1 0 1 1 1 0 0 0 0 0 0 1 0 0 0 0
0 0 1 1 0 1 1 1 0 0 1 0 0 0 0 0 0 1 0 0 0
1 0 0 0 1 1 1 0 1 0 1 0 0 0 0 0 0 0 1 0 0
0 1 0 1 1 0 0 1 1 0 1 0 0 0 0 0 0 0 0 1 0
0 1 1 0 1 0 1 0 0 1 1 0 0 0 0 0 0 0 0 0 1
the automorphism group has order 40320
and is strongly generated by the following 10 elements:
(
1 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 0 0 0 0 0 0 
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 1 0 0 0 0 0 
1 1 1 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 1 0 0 0 
0 0 1 0 1 1 0 1 1 1 0 
0 1 0 1 1 0 0 1 1 0 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 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 1 0 0 
1 1 1 0 0 0 1 1 1 0 0 
0 0 0 1 0 0 0 0 0 0 0 
1 1 1 1 1 1 0 0 0 0 0 
0 0 0 0 1 0 0 0 0 0 0 
0 0 1 1 0 1 1 1 0 0 1 
0 0 1 0 1 1 0 1 1 1 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 1 0 0 0 0 0 0 0 0 
1 0 0 1 1 0 1 1 0 1 0 
0 1 0 1 0 1 1 0 1 1 0 
0 0 0 0 0 0 0 0 0 1 0 
0 1 0 1 1 0 0 1 1 0 1 
0 0 0 0 0 0 0 0 0 0 1 
1 0 0 0 1 1 1 0 1 0 1 
0 0 0 0 0 1 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 1 0 0 0 0 0 0 0 0 0 
0 0 1 0 0 0 0 0 0 0 0 
1 1 1 0 0 0 1 1 1 0 0 
0 0 0 0 0 0 0 1 0 0 0 
0 0 0 0 0 0 1 0 0 0 0 
0 0 0 0 0 1 0 0 0 0 0 
0 0 0 0 1 0 0 0 0 0 0 
1 1 1 1 1 1 0 0 0 0 0 
0 1 0 1 1 0 0 1 1 0 1 
0 1 0 1 0 1 1 0 1 1 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 1 0 0 0 0 0 0 0 0 
1 1 1 1 1 1 0 0 0 0 0 
0 0 0 0 0 1 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 0 0 
0 0 0 0 0 0 1 0 0 0 0 
1 1 1 0 0 0 1 1 1 0 0 
0 1 0 1 0 1 1 0 1 1 0 
0 1 0 1 1 0 0 1 1 0 1 
, 
1 0 0 0 0 0 0 0 0 0 0 
0 1 0 0 0 0 0 0 0 0 0 
1 1 1 1 1 1 1 1 1 1 1 
0 0 1 1 0 1 1 1 0 0 1 
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 1 0 0 1 1 0 1 
1 1 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 1 0 0 0 0 
1 0 0 0 1 1 1 0 1 0 1 
, 
1 0 0 0 0 0 0 0 0 0 0 
1 1 1 1 1 1 1 1 1 1 1 
0 1 0 0 0 0 0 0 0 0 0 
0 1 0 1 0 1 1 0 1 1 0 
1 1 1 0 0 0 1 1 1 0 0 
1 0 0 0 1 1 1 0 1 0 1 
0 0 0 0 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 0 0 0 
0 0 1 1 0 1 1 1 0 0 1 
0 0 0 0 0 0 0 1 0 0 0 
, 
1 0 0 0 0 0 0 0 0 0 0 
1 1 1 1 1 1 0 0 0 0 0 
0 0 0 0 0 0 0 0 1 0 0 
0 0 0 0 0 0 1 0 0 0 0 
0 1 0 1 1 0 0 1 1 0 1 
0 0 0 1 0 0 0 0 0 0 0 
1 1 1 0 0 0 1 1 1 0 0 
1 0 0 1 1 0 1 1 0 1 0 
0 0 0 0 0 0 0 0 0 1 0 
0 0 1 0 1 1 0 1 1 1 0 
0 1 1 0 1 0 1 0 0 1 1 
, 
0 0 0 0 0 0 0 0 1 0 0 
0 1 0 1 1 0 0 1 1 0 1 
0 1 0 1 0 1 1 0 1 1 0 
0 0 0 0 1 0 0 0 0 0 0 
0 0 0 0 0 1 0 0 0 0 0 
1 1 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 1 0 
1 0 0 0 1 1 1 0 1 0 1 
0 0 1 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 1 0 0 1 1 
0 1 0 1 1 0 0 1 1 0 1 
0 0 0 1 0 0 0 0 0 0 0 
1 1 1 1 1 1 1 1 1 1 1 
1 1 1 1 1 1 0 0 0 0 0 
0 0 1 0 0 0 0 0 0 0 0 
1 0 0 0 0 0 0 0 0 0 0 
1 1 1 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 1 0 0 0 0 
0 0 1 1 0 1 1 1 0 0 1 
)
acting on the columns of the generator matrix as follows (in order):
(7, 14)(8, 9)(10, 17)(11, 20)(12, 21)(15, 16)(18, 19), 
(4, 7)(5, 9)(6, 14)(8, 13)(10, 18)(11, 17)(15, 20)(16, 19), 
(4, 15)(5, 16)(6, 10)(7, 20)(8, 11)(9, 19)(13, 17)(14, 18), 
(4, 14)(5, 8)(6, 7)(9, 13)(10, 20)(11, 16)(15, 18)(17, 19), 
(4, 13)(5, 6)(7, 8)(9, 14)(10, 16)(11, 20)(15, 17)(18, 19), 
(3, 12)(4, 15, 14, 18)(5, 13, 8, 9)(6, 20, 7, 10)(11, 17, 16, 19), 
(2, 3, 12)(4, 9, 16)(5, 17, 14)(6, 13, 19)(7, 8, 11)(10, 15, 18), 
(2, 19, 15, 8, 21, 11, 18, 13)(3, 16, 20, 5, 12, 17, 10, 9)(4, 6, 14, 7), 
(1, 14, 18, 19, 9)(2, 11, 17, 15, 20)(3, 10, 8, 7, 16)(4, 12, 13, 6, 5), 
(1, 7, 10, 9, 21)(2, 14, 8, 19, 20)(3, 6, 16, 12, 4)(5, 15, 18, 11, 13)
orbits: { 1, 9, 21, 8, 5, 19, 13, 14, 4, 10, 12, 11, 7, 15, 16, 6, 20, 18, 17, 2, 3 }