The generator matrix 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X X X X X 1 1 1 1 X 1 1 2 X 1 X 1 1 X X 1 1 1 X 2 1 1 1 1 1 X 2 X 1 1 X 1 1 1 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 0 0 2 2 2 0 2 2 2 0 2 0 2 0 2 0 0 0 2 2 0 2 2 2 0 0 2 2 2 0 2 0 0 2 2 2 0 0 2 0 2 2 2 2 0 2 2 2 0 2 0 2 2 2 0 0 0 0 2 0 0 0 0 0 0 0 0 0 2 0 0 2 2 2 2 2 2 0 0 0 0 0 2 2 2 2 2 0 2 0 2 2 2 0 2 0 0 2 0 0 0 0 0 0 2 0 2 2 0 0 2 2 2 2 2 0 2 0 0 2 2 2 0 2 0 0 0 2 2 2 2 0 0 0 0 0 2 0 0 0 0 0 0 0 0 2 2 2 2 2 0 2 2 2 0 2 2 2 0 2 0 0 2 2 2 0 0 2 0 0 0 0 0 2 2 0 2 2 2 2 2 2 0 2 0 2 0 0 2 0 0 0 0 0 2 0 2 2 2 0 2 2 0 2 0 2 2 2 0 0 0 0 0 0 2 0 0 0 0 0 0 2 0 2 2 0 2 2 2 0 2 2 2 0 0 0 0 0 2 0 0 0 2 2 2 2 0 0 0 0 2 0 2 2 0 0 2 2 0 2 0 0 0 0 0 2 2 2 2 0 0 0 2 0 0 2 2 2 2 2 2 2 2 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 2 0 0 2 2 2 2 2 0 0 2 0 0 2 2 0 0 0 2 2 0 0 2 0 0 2 0 0 2 0 2 2 2 0 2 0 2 2 2 0 2 2 2 0 2 2 0 2 0 2 2 0 0 0 2 0 2 2 0 0 2 2 2 0 0 0 0 0 0 0 0 0 2 0 0 0 2 0 0 0 2 2 0 0 2 0 0 2 2 0 2 0 2 0 2 0 2 0 2 0 2 0 0 2 2 2 0 0 0 2 0 2 2 0 0 2 2 0 2 0 2 2 2 2 2 2 2 2 2 0 0 0 0 0 0 0 0 2 0 2 2 0 0 0 0 0 0 0 0 0 2 0 0 2 0 0 2 0 0 2 0 0 2 0 2 2 0 0 2 2 2 0 0 2 2 2 0 0 2 2 0 2 2 0 0 2 2 0 0 2 2 0 0 2 0 0 0 2 2 2 0 0 2 0 0 0 2 0 2 0 0 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 2 2 2 2 0 0 0 0 2 0 0 0 2 2 2 2 0 0 0 2 0 2 0 0 0 2 0 2 2 0 2 0 2 0 0 2 2 2 2 2 2 0 0 0 0 0 2 2 0 2 0 2 2 2 0 2 2 0 0 2 0 2 2 0 0 2 2 0 0 0 0 0 0 0 0 0 2 2 2 2 0 0 2 2 2 2 2 0 2 0 2 0 2 0 2 2 0 0 2 2 2 2 2 2 2 0 2 0 0 0 2 0 2 2 2 2 2 2 0 0 2 2 0 2 2 2 0 2 0 0 0 0 2 2 0 0 2 0 2 0 0 2 0 0 generates a code of length 77 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 64. Homogenous weight enumerator: w(x)=1x^0+87x^64+2x^66+183x^68+62x^70+294x^72+396x^74+1103x^76+948x^78+533x^80+114x^82+163x^84+14x^86+112x^88+49x^92+27x^96+6x^100+1x^104+1x^120 The gray image is a code over GF(2) with n=308, k=12 and d=128. This code was found by Heurico 1.16 in 2.38 seconds.