the 2 isometry classes of irreducible [28,25,3]_5 codes are:

code no       1:
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1 1 1 4 0 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 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 1 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
3 1 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
4 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 0 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 0 1 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
3 0 1 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
4 0 1 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 1 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 1 1 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0
3 1 1 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0
4 1 1 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0
0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0
1 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0
2 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0
3 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0
4 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0
0 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0
1 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0
2 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0
3 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0
4 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0
0 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0
1 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4
the automorphism group has order 600
and is strongly generated by the following 6 elements:
(
2 0 0 
0 1 0 
0 4 2 
, 
3 0 0 
0 3 0 
2 1 2 
, 
1 0 0 
1 3 1 
1 2 2 
, 
3 0 0 
3 2 4 
3 4 2 
, 
0 1 4 
1 1 1 
0 1 1 
, 
2 3 2 
0 4 4 
3 4 4 
)
acting on the columns of the generator matrix as follows (in order):
(3, 13, 22, 17)(4, 23, 18, 9)(5, 7, 8, 6)(10, 14, 24, 19)(11, 15, 25, 20)(12, 16, 26, 21), 
(3, 23)(4, 17)(9, 22)(10, 26)(11, 25)(12, 24)(13, 18)(14, 21)(15, 20)(16, 19)(27, 28), 
(2, 23)(3, 15)(4, 9)(5, 24)(6, 25)(7, 26)(8, 22)(10, 16)(11, 14)(12, 13)(17, 19)(20, 21), 
(2, 19, 10, 24)(3, 23, 6, 21)(4, 13, 15, 16)(5, 20, 9, 26)(7, 17, 12, 25)(8, 18, 11, 22), 
(1, 27)(2, 9, 23, 4)(3, 12, 15, 13)(5, 26, 24, 7)(6, 20, 25, 21)(8, 14, 22, 11)(10, 19, 16, 17), 
(1, 27, 28)(2, 4, 13)(3, 18, 14)(5, 24, 19)(6, 7, 11)(8, 21, 26)(9, 16, 17)(10, 25, 12)(15, 22, 23)
orbits: { 1, 27, 28 }, { 2, 23, 24, 4, 13, 3, 9, 22, 14, 12, 5, 10, 26, 17, 16, 18, 15, 21, 20, 8, 11, 25, 6, 7, 19 }

code no       2:
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1 1 1 4 0 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 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 1 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
3 1 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
4 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 0 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 0 1 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
3 0 1 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
4 0 1 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 1 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 1 1 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0
3 1 1 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0
4 1 1 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0
0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0
1 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0
2 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0
3 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0
4 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0
0 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0
1 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0
2 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0
3 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0
0 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0
1 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0
2 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4
the automorphism group has order 96
and is strongly generated by the following 5 elements:
(
1 0 0 
3 2 2 
3 1 3 
, 
2 0 0 
2 1 3 
2 4 0 
, 
2 0 0 
2 3 0 
3 0 3 
, 
4 1 4 
4 4 4 
4 3 0 
, 
0 1 0 
3 3 3 
4 1 2 
)
acting on the columns of the generator matrix as follows (in order):
(2, 16)(3, 18)(4, 8)(5, 14)(6, 13)(7, 15)(9, 20)(10, 17)(11, 19)(12, 21)(22, 25)(23, 24), 
(2, 12, 16, 21)(3, 15, 18, 7)(4, 17, 8, 10)(5, 9, 14, 20)(6, 11, 13, 19)(22, 23, 25, 24), 
(2, 8)(3, 9)(4, 16)(5, 7)(10, 12)(14, 15)(17, 21)(18, 20)(22, 25)(23, 24)(26, 28), 
(1, 27)(2, 8, 16, 4)(3, 15, 18, 7)(5, 20, 14, 9)(6, 24, 13, 23)(10, 21, 17, 12)(11, 22, 19, 25), 
(1, 4, 2)(3, 20, 24)(5, 15, 23)(6, 14, 9)(7, 13, 18)(8, 16, 27)(10, 12, 28)(11, 22, 19)(17, 21, 26)
orbits: { 1, 27, 2, 16, 21, 8, 4, 12, 17, 10, 26, 28 }, { 3, 18, 7, 9, 24, 15, 20, 13, 5, 14, 23, 25, 6, 11, 22, 19 }