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 X 1 0 1 1 X 0 1 X 1 0 1 1 1 1 X 1 1 0 1 1 1 X 1 1 X 1 1 X 1 X 0 1 0 0 1 X X 2 1 X X 0 1 1 X 0 X 0 X+2 0 X+2 0 X+2 0 X+2 2 X+2 0 X+2 X 0 2 X+2 2 X 0 X 0 2 X+2 2 0 2 X+2 X+2 X X 0 X+2 0 X+2 X+2 0 X X+2 X+2 X+2 X X+2 X+2 0 X 2 0 2 2 X+2 0 2 X 0 X+2 X X+2 X X+2 X+2 0 2 0 X+2 X+2 X X X X 2 X X+2 X X+2 X+2 X+2 X X 2 X+2 0 0 2 0 0 0 0 0 0 0 2 0 2 0 0 0 2 2 0 2 2 2 0 2 2 2 2 0 0 2 2 0 0 0 0 0 0 2 2 2 0 2 2 0 0 0 0 0 2 2 0 2 0 0 0 2 0 2 2 0 2 0 2 0 2 2 2 2 2 2 0 0 0 0 2 0 2 0 2 0 2 2 0 0 0 2 0 0 0 0 0 0 0 2 0 0 2 0 0 2 0 0 2 2 2 2 2 2 2 2 0 0 2 2 0 0 0 0 2 0 0 0 2 2 2 0 2 2 2 0 0 2 2 2 0 2 2 2 0 2 0 0 0 0 0 0 2 2 0 0 0 2 0 2 0 2 0 2 0 0 2 0 0 2 0 0 0 0 2 0 0 0 0 0 0 0 2 0 0 2 0 2 2 2 2 2 2 2 2 0 2 0 0 2 2 0 0 2 2 2 0 0 2 0 2 2 2 2 0 2 0 0 0 2 2 2 2 2 0 0 2 2 0 0 2 2 2 2 0 0 0 2 0 0 0 2 2 0 2 2 0 0 2 2 0 2 0 0 0 0 0 2 0 0 0 2 0 2 0 2 0 2 2 2 0 0 2 2 0 2 0 0 2 2 0 2 2 0 0 2 2 0 2 2 0 2 2 0 0 2 0 2 2 2 0 0 2 0 0 0 2 0 2 2 2 2 0 0 2 0 2 2 2 0 0 2 0 2 0 0 2 2 2 0 2 2 2 0 0 0 0 0 0 0 2 0 0 0 0 0 2 0 0 2 2 0 0 0 0 0 2 2 0 2 0 2 2 2 2 2 0 0 0 2 2 2 0 0 0 2 2 2 0 0 2 0 2 2 2 0 0 2 0 2 0 0 0 2 2 0 2 2 2 0 0 0 2 0 0 2 2 2 0 0 2 2 2 2 0 2 0 0 0 0 0 0 0 2 0 2 0 0 0 0 2 2 2 2 0 2 0 2 2 0 0 2 0 0 0 2 0 2 2 0 0 2 2 0 2 2 2 0 2 2 0 2 0 2 2 0 0 2 2 0 0 0 2 0 0 0 2 0 0 0 2 2 0 0 0 2 0 2 0 2 2 2 0 2 0 0 2 0 0 0 0 0 0 0 0 0 2 0 2 2 2 2 2 0 0 2 2 2 0 0 0 2 2 0 2 0 2 2 0 0 2 0 0 0 2 0 0 2 2 0 0 2 2 2 0 2 2 2 0 0 0 2 0 2 2 0 0 0 2 2 0 2 2 2 2 2 2 2 0 2 0 0 0 0 0 0 0 0 2 0 generates a code of length 82 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 72. Homogenous weight enumerator: w(x)=1x^0+143x^72+142x^74+16x^75+343x^76+80x^77+278x^78+176x^79+478x^80+240x^81+380x^82+240x^83+415x^84+176x^85+348x^86+80x^87+268x^88+16x^89+118x^90+87x^92+14x^94+32x^96+17x^100+4x^104+2x^108+1x^112+1x^120 The gray image is a code over GF(2) with n=328, k=12 and d=144. This code was found by Heurico 1.16 in 2.5 seconds.