the 1 isometry classes of irreducible [22,11,7]_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 0
1 1 1 1 1 1 0 0 0 0 0 0 1 0 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 0
1 0 0 1 1 0 1 1 0 1 0 0 0 0 1 0 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 0 1 0 1 1 0 1 1 1 0 0 0 0 0 0 1 0 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 0
1 0 0 0 1 1 1 0 1 0 1 0 0 0 0 0 0 0 1 0 0 0
0 1 0 1 1 0 0 1 1 0 1 0 0 0 0 0 0 0 0 1 0 0
0 1 1 0 1 0 1 0 0 1 1 0 0 0 0 0 0 0 0 0 1 0
1 1 0 0 0 1 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 1
the automorphism group has order 443520
and is strongly generated by the following 11 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 
1 1 1 1 1 1 0 0 0 0 0 
0 0 0 0 1 0 0 0 0 0 0 
0 1 0 1 1 0 0 1 1 0 1 
0 0 1 1 0 1 1 1 0 0 1 
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 0 0 0 0 0 0 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 
0 0 0 0 0 0 0 0 0 0 1 
0 0 1 1 0 1 1 1 0 0 1 
1 0 0 0 1 1 1 0 1 0 1 
0 0 1 0 1 1 0 1 1 1 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 0 0 0 0 0 0 1 0 0 
0 0 0 1 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 
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 
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 
0 1 0 1 0 1 1 0 1 1 0 
1 0 0 1 1 0 1 1 0 1 0 
0 0 1 0 1 1 0 1 1 1 0 
1 0 0 0 1 1 1 0 1 0 1 
0 0 1 1 0 1 1 1 0 0 1 
0 1 0 1 1 0 0 1 1 0 1 
1 1 1 1 1 1 0 0 0 0 0 
1 1 1 0 0 0 1 1 1 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 1 1 0 1 0 1 0 0 1 1 
0 0 1 1 0 1 1 1 0 0 1 
0 0 0 0 0 0 1 0 0 0 0 
1 0 0 1 1 0 1 1 0 1 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 
0 0 0 0 0 0 0 0 1 0 0 
1 0 0 0 1 1 1 0 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 0 0 0 1 1 1 0 0 
0 1 0 1 0 1 1 0 1 1 0 
0 0 0 0 0 1 0 0 0 0 0 
1 1 1 1 1 1 1 1 1 1 1 
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 0 0 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 
, 
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 0 0 0 
0 0 0 0 0 0 0 0 0 1 0 
0 0 0 0 0 0 1 0 0 0 0 
1 0 0 1 1 0 1 1 0 1 0 
0 0 1 1 0 1 1 1 0 0 1 
1 1 1 0 0 0 1 1 1 0 0 
0 0 0 0 0 1 0 0 0 0 0 
0 1 0 1 0 1 1 0 1 1 0 
0 1 1 0 1 0 1 0 0 1 1 
, 
1 0 0 0 0 0 0 0 0 0 0 
0 0 1 0 1 1 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 1 0 
0 0 0 0 1 0 0 0 0 0 0 
0 1 0 1 1 0 0 1 1 0 1 
1 0 0 1 1 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 1 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 1 0 0 0 0 0 0 
0 0 0 0 0 0 1 0 0 0 0 
1 0 0 1 1 0 1 1 0 1 0 
0 0 1 1 0 1 1 1 0 0 1 
0 0 0 0 0 0 0 0 0 0 1 
1 1 1 1 1 1 1 1 1 1 1 
1 1 1 0 0 0 1 1 1 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 0 0 0 0 1 0 0 
0 0 0 1 0 0 0 0 0 0 0 
, 
1 1 0 0 0 1 0 1 0 1 1 
0 0 1 0 1 1 0 1 1 1 0 
1 0 0 0 1 1 1 0 1 0 1 
1 1 1 0 0 0 1 1 1 0 0 
0 0 0 1 0 0 0 0 0 0 0 
0 1 1 0 1 0 1 0 0 1 1 
1 1 1 1 1 1 0 0 0 0 0 
1 0 0 1 1 0 1 1 0 1 0 
0 0 0 0 0 0 0 1 0 0 0 
0 1 0 1 1 0 0 1 1 0 1 
0 1 0 0 0 0 0 0 0 0 0 
)
acting on the columns of the generator matrix as follows (in order):
(5, 6, 13)(7, 15, 20)(8, 16, 18)(9, 10, 11)(12, 22, 21)(14, 17, 19), 
(4, 11)(5, 18)(6, 19)(7, 17)(8, 15)(9, 10)(13, 20)(14, 16), 
(4, 13)(5, 6)(7, 8)(9, 14)(10, 16)(11, 20)(15, 17)(18, 19), 
(4, 7)(5, 9)(6, 14)(8, 13)(10, 18)(11, 17)(15, 20)(16, 19), 
(4, 16)(5, 15)(6, 17)(7, 19)(8, 18)(9, 20)(10, 13)(11, 14), 
(3, 12, 21)(4, 8, 18)(5, 20, 7)(6, 13, 15)(9, 10, 14)(11, 17, 19), 
(3, 9, 14)(4, 18, 16)(5, 12, 6)(10, 19, 13)(11, 21, 20)(15, 22, 17), 
(2, 19, 20, 14, 8)(3, 17, 18, 7, 5)(4, 13, 12, 16, 10)(6, 9, 21, 11, 15), 
(2, 17)(3, 11)(4, 10)(6, 20)(7, 15)(12, 16)(14, 18)(19, 21), 
(1, 18, 4, 11, 5)(2, 17, 16, 14, 7)(3, 8, 20, 13, 15)(6, 9, 10, 19, 12), 
(1, 12, 13, 7, 19, 3, 18, 17, 2, 11, 22)(4, 5, 15, 8, 9, 16, 21, 6, 20, 10, 14)
orbits: { 1, 5, 22, 13, 18, 6, 9, 15, 7, 11, 4, 12, 20, 8, 10, 19, 16, 17, 14, 3, 21, 2 }