the 1 isometry classes of irreducible [30,24,4]_2 codes are:

code no       1:
================
1 1 1 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
1 1 0 1 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 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 1 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
1 1 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 0
1 0 1 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 1 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
1 0 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 0 0
0 1 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 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
1 1 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
1 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 0
1 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 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
1 0 0 1 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 1 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 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 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
1 0 0 0 1 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 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 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
1 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 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 1 0
1 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 1
the automorphism group has order 645120
and is strongly generated by the following 12 elements:
(
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
0 0 0 1 0 0 
0 0 0 0 1 0 
1 1 0 0 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
0 0 0 1 0 0 
1 0 1 0 1 0 
1 0 1 0 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
0 0 0 1 0 0 
0 1 1 0 0 1 
0 1 1 0 1 0 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
0 0 0 1 0 0 
1 1 0 0 1 0 
1 1 0 0 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
0 0 0 1 0 0 
0 0 1 1 0 1 
0 0 1 1 1 0 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
1 0 1 1 0 0 
0 1 0 1 1 0 
1 1 1 1 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
1 1 0 0 1 0 
1 0 1 0 0 1 
0 1 1 1 0 0 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
1 1 1 0 0 0 
0 0 1 1 0 1 
1 1 0 1 0 0 
1 1 1 1 1 0 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 1 1 0 1 0 
0 0 1 0 0 0 
0 1 0 0 1 1 
0 0 1 1 1 0 
, 
0 0 1 0 0 0 
1 1 1 0 0 0 
1 0 0 0 0 0 
0 0 0 1 0 0 
0 1 0 1 0 1 
0 1 0 1 1 0 
, 
1 1 1 0 1 1 
0 0 1 0 1 1 
1 0 0 0 1 1 
0 1 0 0 0 0 
1 0 0 1 1 0 
1 1 0 0 0 1 
, 
1 1 0 1 1 1 
0 0 0 1 1 1 
1 1 1 0 0 0 
0 0 0 0 0 1 
0 1 0 0 1 1 
1 1 0 0 1 0 
)
acting on the columns of the generator matrix as follows (in order):
(6, 18)(19, 20)(21, 22)(23, 24)(25, 26)(27, 28)(29, 30), 
(5, 12)(6, 19)(11, 13)(14, 16)(15, 17)(18, 20)(21, 23)(22, 24), 
(5, 20)(6, 13)(11, 19)(12, 18)(14, 24)(15, 23)(16, 22)(17, 21), 
(5, 11)(6, 18)(12, 13)(14, 15)(16, 17)(19, 20)(21, 22)(23, 24), 
(5, 23)(6, 16)(11, 24)(12, 21)(13, 22)(14, 19)(15, 20)(17, 18), 
(4, 9)(5, 17, 12, 15)(6, 22, 19, 24)(8, 10)(11, 16, 13, 14)(18, 21, 20, 23)(25, 27)(26, 28), 
(4, 20, 11)(5, 8, 19)(6, 12, 10)(9, 18, 13)(14, 23, 28)(15, 24, 27)(16, 21, 26)(17, 22, 25), 
(3, 7)(4, 11, 27, 23)(5, 28, 24, 8)(6, 16, 18, 17)(9, 12, 25, 22)(10, 13, 26, 21)(14, 19, 15, 20), 
(3, 4, 20, 13)(5, 10, 23, 26)(6, 16)(7, 8, 19, 12)(9, 24, 25, 11)(14, 21, 30, 28)(15, 22, 29, 27)(17, 18), 
(1, 3)(2, 7)(5, 24, 12, 22)(6, 17, 19, 15)(11, 23, 13, 21)(14, 18, 16, 20)(25, 27)(26, 28), 
(1, 8, 27, 2, 4, 28)(3, 9, 25)(5, 23, 14)(6, 18)(7, 10, 26)(11, 24, 15)(12, 22, 16, 13, 21, 17), 
(1, 29, 2, 30)(3, 7)(4, 21, 14, 26, 5, 18, 8, 22, 15, 25, 11, 6)(9, 13, 17, 10, 12, 16)(19, 28, 24)(20, 27, 23)
orbits: { 1, 3, 28, 30, 7, 13, 25, 27, 26, 23, 5, 4, 19, 29, 21, 2, 12, 11, 6, 22, 16, 18, 10, 20, 9, 24, 15, 8, 14, 17 }