the 1 isometry classes of irreducible [20,9,7]_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
1 1 1 1 1 1 0 0 0 0 0 0 1 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
1 0 0 1 1 0 1 1 0 1 0 0 0 0 1 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 1 0 1 1 0 1 1 1 0 0 0 0 0 0 1 0 0 0
0 0 1 1 0 1 1 1 0 0 1 0 0 0 0 0 0 1 0 0
1 0 0 0 1 1 1 0 1 0 1 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 1
the automorphism group has order 5760
and is strongly generated by the following 8 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 0 1 0 0 0 0 0 
1 1 1 1 1 1 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 1 0 
0 1 0 1 0 1 1 0 1 1 0 
1 0 0 0 1 1 1 0 1 0 1 
0 0 0 0 0 0 1 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 1 0 1 0 1 1 0 1 1 0 
0 0 1 0 1 1 0 1 1 1 0 
0 0 0 0 0 0 0 0 0 1 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 1 0 0 0 0 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 
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 1 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 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 1 0 0 0 0 
1 0 0 1 1 0 1 1 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 
1 1 1 1 1 1 1 1 1 1 1 
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 0 1 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 1 0 0 0 
, 
1 0 0 0 0 0 0 0 0 0 0 
1 1 1 1 1 1 1 1 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 
1 1 1 0 0 0 1 1 1 0 0 
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 1 0 0 0 
0 1 0 1 0 1 1 0 1 1 0 
1 0 0 0 1 1 1 0 1 0 1 
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 1 0 0 0 0 0 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 0 0 0 0 1 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 1 0 0 0 0 0 0 0 
1 0 0 1 1 0 1 1 0 1 0 
1 0 0 0 1 1 1 0 1 0 1 
, 
1 0 0 0 1 1 1 0 1 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 1 0 0 
0 0 0 0 0 0 0 0 0 0 1 
1 0 0 0 0 0 0 0 0 0 0 
1 1 1 0 0 0 1 1 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 1 0 1 1 0 1 1 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 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 
)
acting on the columns of the generator matrix as follows (in order):
(5, 13, 6)(7, 11, 17)(8, 19, 10)(9, 20, 16)(14, 18, 15), 
(4, 9, 16)(5, 14, 17)(6, 7, 10)(8, 15, 13)(11, 18, 19), 
(4, 5, 13)(7, 10, 20)(8, 17, 18)(9, 15, 11)(14, 16, 19), 
(3, 12)(4, 9)(6, 10)(8, 11)(13, 18)(14, 17)(15, 19), 
(2, 12)(5, 14)(6, 18)(7, 11)(9, 16)(10, 19)(13, 15), 
(2, 3)(4, 9)(5, 14)(6, 8)(7, 13)(10, 15)(11, 19), 
(1, 6, 13, 19)(2, 8, 11, 5)(3, 18, 14, 7)(4, 9)(10, 15, 12, 17), 
(1, 14, 18, 19, 9)(2, 11, 17, 15, 20)(3, 10, 8, 7, 16)(4, 12, 13, 6, 5)
orbits: { 1, 19, 9, 8, 18, 16, 15, 10, 11, 13, 4, 6, 2, 14, 17, 3, 20, 7, 5, 12 }