the 1 isometry classes of irreducible [4,1,4]_27 codes are: code no 1: ================ 1 1 1 2 the automorphism group has order 72 and is strongly generated by the following 6 elements: ( 3 0 0 0 3 0 0 0 3 , 2 , 25 0 0 0 25 0 14 14 14 , 0 , 7 0 0 0 0 7 0 7 0 , 2 , 15 0 0 21 21 21 0 15 0 , 2 , 0 0 15 15 0 0 0 15 0 , 1 , 1 1 1 2 0 0 0 2 0 , 2 ) acting on the columns of the generator matrix as follows (in order): id, (3, 4), (2, 3), (2, 3, 4), (1, 2, 3), (1, 2, 3, 4) orbits: { 1, 3, 4, 2 }