the 10 isometry classes of irreducible [14,11,3]_4 codes are: code no 1: ================ 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 2 1 0 0 0 1 0 0 0 0 0 0 0 0 3 1 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 0 0 0 0 0 0 2 0 1 0 0 0 0 0 1 0 0 0 0 0 3 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 0 0 0 2 1 1 0 0 0 0 0 0 0 0 1 0 0 3 1 1 0 0 0 0 0 0 0 0 0 1 0 0 2 1 0 0 0 0 0 0 0 0 0 0 1 the automorphism group has order 72 and is strongly generated by the following 3 elements: ( 2 0 0 0 1 0 0 0 1 , 0 , 1 0 0 0 1 0 0 1 1 , 1 , 1 0 0 1 2 2 2 2 0 , 0 ) acting on the columns of the generator matrix as follows (in order): (4, 13, 12)(5, 7, 6)(8, 10, 9), (3, 11)(4, 8)(6, 7)(9, 13)(10, 12), (2, 9, 11, 5, 3, 13)(4, 7, 10, 12, 6, 8) orbits: { 1 }, { 2, 13, 4, 9, 3, 12, 8, 10, 11, 5, 6, 7 }, { 14 } code no 2: ================ 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 2 1 0 0 0 1 0 0 0 0 0 0 0 0 3 1 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 0 0 0 0 0 0 2 0 1 0 0 0 0 0 1 0 0 0 0 0 3 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 0 0 0 2 1 1 0 0 0 0 0 0 0 0 1 0 0 0 2 1 0 0 0 0 0 0 0 0 0 1 0 1 2 1 0 0 0 0 0 0 0 0 0 0 1 the automorphism group has order 4 and is strongly generated by the following 2 elements: ( 1 0 0 3 0 3 1 3 0 , 1 , 3 0 0 1 3 0 1 0 3 , 0 ) acting on the columns of the generator matrix as follows (in order): (2, 8)(3, 7)(5, 9)(6, 10)(11, 12), (2, 6)(3, 9)(5, 7)(8, 10)(13, 14) orbits: { 1 }, { 2, 8, 6, 10 }, { 3, 7, 9, 5 }, { 4 }, { 11, 12 }, { 13, 14 } code no 3: ================ 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 2 1 0 0 0 1 0 0 0 0 0 0 0 0 3 1 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 0 0 0 0 0 0 2 0 1 0 0 0 0 0 1 0 0 0 0 0 3 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 0 0 0 2 1 1 0 0 0 0 0 0 0 0 1 0 0 0 2 1 0 0 0 0 0 0 0 0 0 1 0 0 3 1 0 0 0 0 0 0 0 0 0 0 1 the automorphism group has order 4 and is strongly generated by the following 2 elements: ( 3 0 0 0 1 0 0 0 1 , 1 , 3 0 0 0 0 1 0 1 0 , 1 ) acting on the columns of the generator matrix as follows (in order): (4, 12)(5, 6)(8, 9)(13, 14), (2, 3)(4, 12)(5, 9)(6, 8)(7, 10) orbits: { 1 }, { 2, 3 }, { 4, 12 }, { 5, 6, 9, 8 }, { 7, 10 }, { 11 }, { 13, 14 } code no 4: ================ 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 2 1 0 0 0 1 0 0 0 0 0 0 0 0 3 1 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 0 0 0 0 0 0 2 0 1 0 0 0 0 0 1 0 0 0 0 0 3 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 0 0 0 2 1 1 0 0 0 0 0 0 0 0 1 0 0 0 2 1 0 0 0 0 0 0 0 0 0 1 0 1 3 1 0 0 0 0 0 0 0 0 0 0 1 the automorphism group has order 12 and is strongly generated by the following 3 elements: ( 1 0 0 0 1 0 1 0 1 , 1 , 3 0 0 0 0 1 0 1 0 , 1 , 1 0 0 3 0 3 1 3 0 , 1 ) acting on the columns of the generator matrix as follows (in order): (3, 8)(4, 11)(6, 7)(13, 14), (2, 3)(4, 12)(5, 9)(6, 8)(7, 10), (2, 8)(3, 7)(5, 9)(6, 10)(11, 12) orbits: { 1 }, { 2, 3, 8, 7, 6, 10 }, { 4, 11, 12 }, { 5, 9 }, { 13, 14 } code no 5: ================ 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 2 1 0 0 0 1 0 0 0 0 0 0 0 0 3 1 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 0 0 0 0 0 0 2 0 1 0 0 0 0 0 1 0 0 0 0 0 3 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 0 0 0 0 2 1 0 0 0 0 0 0 0 0 1 0 0 3 2 1 0 0 0 0 0 0 0 0 0 1 0 0 3 1 0 0 0 0 0 0 0 0 0 0 1 the automorphism group has order 48 and is strongly generated by the following 4 elements: ( 2 0 0 0 3 0 0 0 1 , 1 , 1 0 0 0 0 1 0 1 0 , 1 , 2 0 0 1 3 0 3 0 1 , 1 , 2 0 1 0 2 3 0 0 2 , 0 ) acting on the columns of the generator matrix as follows (in order): (4, 13)(5, 6)(8, 10)(11, 12), (2, 3)(5, 8)(6, 10)(7, 9), (2, 7)(3, 9)(4, 12)(11, 13), (1, 9)(2, 14)(4, 5)(6, 13)(8, 10)(11, 12) orbits: { 1, 9, 7, 3, 2, 14 }, { 4, 13, 12, 5, 11, 6, 8, 10 } code no 6: ================ 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 2 1 0 0 0 1 0 0 0 0 0 0 0 0 3 1 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 0 0 0 0 0 0 2 0 1 0 0 0 0 0 1 0 0 0 0 0 3 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 0 0 0 0 2 1 0 0 0 0 0 0 0 0 1 0 0 3 2 1 0 0 0 0 0 0 0 0 0 1 0 1 3 1 0 0 0 0 0 0 0 0 0 0 1 the automorphism group has order 8 and is strongly generated by the following 2 elements: ( 3 0 0 3 0 3 3 3 0 , 1 , 2 0 0 3 3 0 1 0 1 , 1 ) acting on the columns of the generator matrix as follows (in order): (2, 8)(3, 5)(6, 9)(7, 10)(12, 13), (2, 6, 7, 5)(3, 10, 9, 8)(4, 13, 11, 12) orbits: { 1 }, { 2, 8, 5, 9, 3, 7, 6, 10 }, { 4, 12, 13, 11 }, { 14 } code no 7: ================ 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 2 1 0 0 0 1 0 0 0 0 0 0 0 0 3 1 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 0 0 0 0 0 0 2 0 1 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 0 0 0 0 2 1 1 0 0 0 0 0 0 0 1 0 0 0 0 2 1 0 0 0 0 0 0 0 0 1 0 0 1 2 1 0 0 0 0 0 0 0 0 0 1 0 2 2 1 0 0 0 0 0 0 0 0 0 0 1 the automorphism group has order 36 and is strongly generated by the following 5 elements: ( 2 0 0 0 2 0 0 0 3 , 1 , 1 0 0 0 1 0 1 1 1 , 1 , 3 0 0 0 2 0 0 3 3 , 0 , 3 0 0 0 3 0 3 3 2 , 0 , 0 3 0 3 0 0 3 3 3 , 1 ) acting on the columns of the generator matrix as follows (in order): (4, 14)(6, 7)(8, 9)(10, 12)(11, 13), (3, 4)(6, 7)(8, 10)(9, 11)(12, 13), (3, 12, 10)(4, 8, 13)(5, 7, 6)(9, 14, 11), (3, 4, 14)(8, 11, 12)(9, 10, 13), (1, 2)(3, 4)(9, 13)(11, 12) orbits: { 1, 2 }, { 3, 4, 10, 14, 13, 12, 8, 9, 11 }, { 5, 6, 7 } code no 8: ================ 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 2 1 0 0 0 1 0 0 0 0 0 0 0 0 3 1 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 0 0 0 0 0 0 2 0 1 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 0 0 0 0 2 1 1 0 0 0 0 0 0 0 1 0 0 0 0 2 1 0 0 0 0 0 0 0 0 1 0 0 1 2 1 0 0 0 0 0 0 0 0 0 1 0 3 2 1 0 0 0 0 0 0 0 0 0 0 1 the automorphism group has order 6 and is strongly generated by the following 2 elements: ( 1 0 0 0 1 0 1 1 1 , 1 , 1 0 0 2 3 0 0 3 2 , 0 ) acting on the columns of the generator matrix as follows (in order): (3, 4)(6, 7)(8, 10)(9, 11)(12, 13), (2, 6, 7)(3, 11, 12)(4, 13, 9)(8, 10, 14) orbits: { 1 }, { 2, 7, 6 }, { 3, 4, 12, 9, 13, 11 }, { 5 }, { 8, 10, 14 } code no 9: ================ 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 2 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 0 0 0 0 2 0 1 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 1 0 0 0 0 0 2 1 1 0 0 0 0 0 0 1 0 0 0 0 0 2 1 0 0 0 0 0 0 0 1 0 0 0 1 3 1 0 0 0 0 0 0 0 0 1 0 0 2 3 1 0 0 0 0 0 0 0 0 0 1 0 3 3 1 0 0 0 0 0 0 0 0 0 0 1 the automorphism group has order 336 and is strongly generated by the following 6 elements: ( 1 0 0 0 2 0 0 2 2 , 1 , 2 0 0 2 1 1 3 0 3 , 0 , 0 3 1 0 3 0 1 1 0 , 1 , 1 0 3 0 3 0 1 0 1 , 0 , 1 2 1 0 3 0 0 0 1 , 1 , 3 3 1 1 3 0 2 0 0 , 0 ) acting on the columns of the generator matrix as follows (in order): (3, 9)(4, 8)(5, 6)(7, 10)(12, 13), (2, 12, 10)(3, 8, 7)(4, 6, 13)(5, 14, 9), (1, 11)(3, 5)(6, 9)(7, 12)(10, 13), (1, 8)(3, 7)(4, 11)(5, 10)(6, 13)(9, 12), (1, 12)(4, 5)(6, 7)(8, 10)(9, 11), (1, 3, 4, 10, 12, 7, 14)(2, 11, 13, 8, 5, 9, 6) orbits: { 1, 11, 8, 12, 14, 4, 9, 2, 3, 10, 13, 7, 5, 6 } code no 10: ================ 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 2 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 0 0 0 0 2 0 1 0 0 0 0 1 0 0 0 0 0 0 2 1 1 0 0 0 0 0 1 0 0 0 0 0 3 1 1 0 0 0 0 0 0 1 0 0 0 0 0 2 1 0 0 0 0 0 0 0 1 0 0 0 1 2 1 0 0 0 0 0 0 0 0 1 0 0 3 2 1 0 0 0 0 0 0 0 0 0 1 0 0 3 1 0 0 0 0 0 0 0 0 0 0 1 the automorphism group has order 48 and is strongly generated by the following 3 elements: ( 2 0 0 0 3 0 0 1 2 , 1 , 2 0 0 1 2 2 3 0 3 , 0 , 0 1 3 3 1 2 1 3 1 , 1 ) acting on the columns of the generator matrix as follows (in order): (3, 11)(5, 6)(7, 12)(8, 13)(9, 10), (2, 13, 10)(3, 8, 7)(4, 6, 11)(5, 12, 9), (1, 14)(2, 13)(3, 12)(4, 6)(5, 8)(7, 9) orbits: { 1, 14 }, { 2, 10, 13, 9, 8, 12, 7, 3, 5, 11, 6, 4 }