the 1 isometry classes of irreducible [22,10,8]_2 codes are:

code no       1:
================
1 1 1 1 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
1 1 1 1 0 0 0 1 1 1 0 0 0 1 0 0 0 0 0 0 0 0
1 1 0 0 1 1 0 1 1 0 1 0 0 0 1 0 0 0 0 0 0 0
1 0 1 0 1 0 1 1 0 1 1 0 0 0 0 1 0 0 0 0 0 0
1 0 0 1 0 1 1 0 1 1 1 0 0 0 0 0 1 0 0 0 0 0
0 1 1 0 1 0 1 1 1 0 0 1 0 0 0 0 0 1 0 0 0 0
1 1 0 0 0 1 1 1 0 1 0 1 0 0 0 0 0 0 1 0 0 0
0 1 0 1 1 1 0 0 1 1 0 1 0 0 0 0 0 0 0 1 0 0
0 0 0 1 1 1 1 1 0 0 1 1 0 0 0 0 0 0 0 0 1 0
1 0 1 1 1 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 1
the automorphism group has order 887040
and is strongly generated by the following 14 elements:
(
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 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 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 0 1 0 0 0 0 
1 1 1 1 0 0 0 1 1 1 0 0 
1 1 0 0 1 1 0 1 1 0 1 0 
0 1 1 0 1 0 1 1 1 0 0 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 0 0 0 0 0 0 0 0 
0 0 0 1 0 0 0 0 0 0 0 0 
0 1 1 0 1 0 1 1 1 0 0 1 
0 0 0 0 0 0 0 0 0 0 0 1 
0 1 0 1 1 1 0 0 1 1 0 1 
1 1 0 0 1 1 0 1 1 0 1 0 
1 0 0 1 0 1 1 0 1 1 1 0 
1 0 1 0 1 0 1 1 0 1 1 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 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 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 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 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 0 0 0 
1 1 0 0 0 1 1 1 0 1 0 1 
1 1 0 0 1 1 0 1 1 0 1 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 0 0 0 0 0 
0 0 0 1 0 0 0 0 0 0 0 0 
1 0 0 1 0 1 1 0 1 1 1 0 
0 0 0 0 0 0 0 0 0 0 1 0 
1 0 1 0 1 0 1 1 0 1 1 0 
1 1 0 0 0 1 1 1 0 1 0 1 
0 1 1 0 1 0 1 1 1 0 0 1 
0 1 0 1 1 1 0 0 1 1 0 1 
0 0 0 0 0 1 0 0 0 0 0 0 
1 1 1 1 0 0 0 1 1 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 1 0 0 0 0 0 0 0 0 0 
0 0 0 1 0 0 0 0 0 0 0 0 
1 1 0 0 1 1 0 1 1 0 1 0 
1 0 1 0 1 0 1 1 0 1 1 0 
0 0 0 0 0 0 0 0 0 0 1 0 
0 1 1 0 1 0 1 1 1 0 0 1 
1 1 0 0 0 1 1 1 0 1 0 1 
0 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 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 
0 0 0 1 1 1 1 1 0 0 1 1 
0 0 0 0 0 0 1 0 0 0 0 0 
0 1 1 0 1 0 1 1 1 0 0 1 
1 0 0 1 0 1 1 0 1 1 1 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 1 0 0 1 1 0 1 1 0 1 0 
0 0 0 0 0 0 0 0 1 0 0 0 
0 0 0 0 0 0 0 1 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 0 1 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 1 1 0 0 1 
0 0 0 0 0 0 0 0 0 0 0 1 
1 1 0 0 0 1 1 1 0 1 0 1 
0 0 0 0 0 0 0 1 0 0 0 0 
1 1 1 1 0 0 0 1 1 1 0 0 
0 0 0 0 0 0 0 0 0 1 0 0 
1 0 0 1 0 1 1 0 1 1 1 0 
0 0 0 0 0 1 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 
1 0 1 1 1 0 0 0 1 0 1 1 
0 0 0 1 1 1 1 1 0 0 1 1 
1 0 1 0 1 0 1 1 0 1 1 0 
1 1 0 0 1 1 0 1 1 0 1 0 
0 0 0 0 0 0 0 0 0 1 0 0 
1 1 0 0 0 1 1 1 0 1 0 1 
0 0 0 0 0 0 1 0 0 0 0 0 
0 1 0 1 1 1 0 0 1 1 0 1 
0 0 0 0 1 0 0 0 0 0 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 
0 1 0 0 0 0 0 0 0 0 0 0 
1 1 1 1 0 0 0 1 1 1 0 0 
0 0 0 0 0 0 0 0 1 0 0 0 
1 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 1 1 1 1 1 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 1 
1 1 0 0 0 1 1 1 0 1 0 1 
0 1 0 1 1 1 0 0 1 1 0 1 
0 0 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 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 0 1 0 0 0 0 0 0 0 
0 0 0 0 0 0 1 0 0 0 0 0 
1 1 1 1 1 1 1 0 0 0 0 0 
0 1 0 1 1 1 0 0 1 1 0 1 
1 1 0 0 0 1 1 1 0 1 0 1 
0 1 1 0 1 0 1 1 1 0 0 1 
0 0 0 0 0 0 0 1 0 0 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 
0 0 0 0 0 1 0 0 0 0 0 0 
0 1 1 0 1 0 1 1 1 0 0 1 
0 0 0 0 0 0 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 1 0 0 
0 0 0 0 1 0 0 0 0 0 0 0 
1 0 0 1 0 1 1 0 1 1 1 0 
1 1 0 0 1 1 0 1 1 0 1 0 
1 0 1 0 1 0 1 1 0 1 1 0 
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 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 0 
1 1 1 1 1 1 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 1 0 0 0 
1 1 1 1 0 0 0 1 1 1 0 0 
0 0 0 0 0 0 0 0 0 0 0 1 
0 1 0 1 1 1 0 0 1 1 0 1 
0 1 1 0 1 0 1 1 1 0 0 1 
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 0 0 1 1 1 1 1 0 0 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 1 0 0 0 0 0 0 
0 0 1 0 0 0 0 0 0 0 0 0 
1 1 1 1 0 0 0 1 1 1 0 0 
1 0 1 0 1 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 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 1 0 0 0 
1 0 0 0 0 0 0 0 0 0 0 0 
, 
1 0 1 1 1 0 0 0 1 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 1 
0 0 0 0 0 0 1 0 0 0 0 0 
0 1 0 1 1 1 0 0 1 1 0 1 
0 0 0 0 1 0 0 0 0 0 0 0 
1 1 1 1 0 0 0 1 1 1 0 0 
1 1 0 0 0 1 1 1 0 1 0 1 
0 1 1 0 1 0 1 1 1 0 0 1 
1 0 0 1 0 1 1 0 1 1 1 0 
0 1 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 1 0 0 
)
acting on the columns of the generator matrix as follows (in order):
(8, 9)(10, 14)(11, 15)(12, 18)(16, 17)(19, 20)(21, 22), 
(5, 18)(6, 12)(7, 20)(8, 15)(9, 17)(10, 16)(11, 14)(13, 19), 
(5, 10)(6, 8)(7, 9)(11, 19)(12, 15)(13, 14)(16, 18)(17, 20), 
(5, 17)(6, 11)(7, 16)(8, 19)(9, 18)(10, 20)(12, 14)(13, 15), 
(5, 15)(6, 16)(7, 11)(8, 18)(9, 19)(10, 12)(13, 17)(14, 20), 
(4, 21)(5, 16, 17, 7)(6, 9, 11, 18)(8, 12, 19, 14)(10, 13, 20, 15), 
(3, 4)(5, 18)(6, 12)(7, 19)(9, 14)(11, 17)(13, 20), 
(3, 21, 4, 22)(5, 11, 18, 15, 6, 17, 12, 16)(7, 9, 19, 8, 13, 14, 20, 10), 
(3, 18, 16, 22, 13, 14)(4, 12, 9)(5, 8, 20, 11, 6, 17)(7, 15, 21)(10, 19), 
(2, 3, 4)(6, 13, 7)(8, 11, 20)(9, 15, 19)(10, 16, 18)(12, 14, 17), 
(2, 12, 16, 10, 6)(3, 5, 7, 20, 18)(4, 17, 8, 15, 9)(11, 21, 14, 19, 13), 
(1, 16, 18, 10, 5)(2, 15, 20, 9, 6)(3, 17, 19, 14, 7)(4, 11, 12, 8, 13), 
(1, 12, 10, 18, 13, 21)(2, 17, 16, 7, 3, 5)(4, 14, 6)(8, 9, 11)(15, 19), 
(1, 14, 7, 4, 19, 8, 18, 9, 2, 11, 15, 22)(3, 21, 13, 17, 10, 12)(5, 6, 16, 20)
orbits: { 1, 5, 21, 22, 18, 10, 17, 15, 7, 16, 3, 20, 4, 11, 13, 12, 9, 8, 14, 19, 6, 2 }