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 X 0 1 1 1 1 X 1 X 1 1 1 1 1 0 1 1 1 0 1 X 1 0 1 X 1 1 1 1 0 1 1 1 2 1 X 1 1 1 X X 1 X 1 X 1 0 1 1 X 1 0 X 0 X+2 0 X+2 0 X+2 0 X+2 2 X+2 0 X+2 X 0 2 2 X+2 X+2 0 0 X+2 X 2 0 2 2 X+2 X X X X+2 X X+2 X+2 X+2 0 X+2 0 0 X+2 X 0 2 X X 0 X+2 0 X 2 X+2 X+2 0 2 2 X X+2 X+2 X X X X+2 2 2 0 X+2 X X+2 X+2 0 X+2 X+2 X X+2 X 0 0 0 0 2 0 0 0 0 0 0 0 2 0 2 2 2 0 2 0 0 0 0 2 2 2 2 0 0 0 2 2 2 0 2 0 2 0 2 0 2 2 2 0 2 0 0 2 0 2 0 0 2 2 0 0 2 0 0 2 2 0 2 2 2 2 0 2 0 2 0 0 0 0 2 0 0 2 2 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 2 2 0 0 0 0 2 0 0 2 0 0 0 0 0 0 0 0 0 2 2 0 2 0 2 2 2 2 2 0 2 2 2 0 2 0 2 0 2 2 2 0 2 0 2 2 0 2 0 2 0 2 2 0 2 2 2 0 2 0 0 0 0 2 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 0 0 2 2 0 0 2 2 0 0 2 0 0 2 0 0 0 0 0 0 0 2 0 0 2 2 2 2 2 2 2 2 2 0 2 0 2 2 0 0 2 0 2 0 2 0 2 0 2 0 2 2 2 0 0 2 2 2 0 2 0 0 2 0 0 0 0 0 0 0 2 0 0 0 2 0 2 0 0 2 0 0 0 0 2 2 2 0 2 2 2 2 2 2 2 0 2 0 2 0 0 0 2 2 0 0 2 0 2 2 0 2 2 2 2 0 0 0 2 0 0 0 0 0 0 2 2 0 2 0 0 2 0 0 0 0 2 0 2 2 0 2 0 0 0 0 0 0 0 0 2 0 0 0 0 0 2 0 0 2 0 2 2 2 0 0 2 2 2 2 2 2 2 2 2 2 2 2 2 0 2 2 0 0 0 0 2 0 0 0 2 2 2 2 2 0 0 2 2 0 2 0 0 2 2 2 2 0 2 0 0 2 2 2 0 2 0 0 0 0 2 2 0 0 0 0 0 0 0 0 2 0 2 0 0 0 2 2 2 2 0 2 2 2 0 0 2 2 2 0 2 0 0 2 2 0 2 0 2 0 0 0 0 2 0 2 2 0 2 0 2 2 0 0 0 0 0 2 2 2 0 0 2 0 2 0 2 2 2 2 2 2 2 2 2 0 2 0 2 2 2 0 0 0 0 0 0 0 0 0 2 0 2 2 2 2 0 2 0 0 0 2 2 2 0 0 2 2 0 0 2 0 0 0 2 0 0 2 2 0 0 0 2 0 0 2 0 2 2 2 2 2 0 2 0 2 2 2 0 0 2 2 2 0 0 2 2 0 0 0 2 0 0 0 2 0 2 2 2 0 2 generates a code of length 79 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 68. Homogenous weight enumerator: w(x)=1x^0+45x^68+26x^69+86x^70+82x^71+118x^72+126x^73+174x^74+222x^75+284x^76+372x^77+339x^78+404x^79+349x^80+332x^81+281x^82+252x^83+148x^84+146x^85+86x^86+58x^87+51x^88+22x^89+35x^90+6x^91+16x^92+15x^94+6x^96+5x^98+3x^100+2x^102+3x^104+1x^122 The gray image is a code over GF(2) with n=316, k=12 and d=136. This code was found by Heurico 1.16 in 2.11 seconds.