The generator matrix 1 0 0 1 1 1 0 1 1 1 1 0 X 1 0 1 0 1 X X 1 1 1 0 1 1 0 1 X X 0 0 1 1 1 X 0 1 X 1 0 X X 1 0 1 X 1 X 0 1 1 1 1 1 1 1 1 0 0 X 1 1 X 1 X 0 X 1 1 X 0 1 1 X X X 0 0 0 1 0 0 1 1 1 0 0 1 X+1 1 1 X 0 X 0 X+1 1 1 X+1 X+1 X 1 0 1 1 X+1 1 0 1 X X+1 X X 1 1 0 1 X+1 X 1 0 0 X 1 1 X+1 1 1 X+1 0 X+1 1 0 0 X 0 X 0 X X X+1 1 X+1 1 1 X X 1 X 1 X+1 X+1 1 1 1 1 X 0 0 1 1 1 0 1 0 1 X+1 0 X X+1 X 1 1 1 X+1 X 1 0 0 X+1 0 X 1 0 X X+1 1 0 1 X 1 0 0 X+1 1 1 0 1 X+1 1 0 1 X X+1 1 X+1 1 X X+1 X+1 X+1 X+1 0 1 0 1 1 1 X 1 1 X 1 X+1 1 1 1 1 0 1 0 0 0 X+1 1 0 0 0 0 X 0 0 0 0 0 X X 0 0 X X 0 0 0 0 X 0 X X 0 X X 0 X X X X 0 X 0 X 0 X 0 0 0 X X 0 0 X 0 X X 0 X X X X 0 X 0 0 0 X X 0 0 0 X X 0 0 X 0 X 0 X 0 X 0 X X 0 X 0 0 0 0 X 0 0 0 0 X 0 0 0 0 0 0 X 0 X X X 0 X 0 X X X X 0 X X 0 X X 0 X 0 0 0 X 0 0 0 0 X X X 0 0 X 0 X X X X 0 X X X 0 X X X X X X 0 X 0 0 0 0 X 0 0 X X X X 0 0 0 0 0 X 0 0 0 0 X 0 0 0 0 0 X X X X X 0 X X 0 X 0 0 0 X 0 X X 0 X X X X 0 0 X 0 X 0 0 0 X 0 X X 0 0 0 X 0 0 X X X X 0 0 0 0 0 X X X 0 X 0 X 0 X 0 X 0 X X 0 0 0 0 0 0 X 0 0 0 0 0 X 0 0 0 0 0 0 X X X 0 X X X X 0 X 0 X X X X X 0 0 X X X 0 0 0 X 0 X 0 0 X 0 0 0 X X 0 X X X X X X 0 0 X 0 0 0 X X X X 0 0 X X X X X X 0 0 0 0 0 0 0 X 0 0 0 X X X X X X 0 0 0 X 0 0 X X X X X 0 0 X 0 X 0 X 0 0 X 0 X X X 0 0 X 0 0 X 0 0 0 X 0 0 0 0 X 0 X 0 X 0 X X 0 X X X 0 X 0 0 0 X 0 X 0 X X 0 0 0 0 0 0 0 0 X X X 0 0 X X X 0 0 0 X X 0 0 X 0 0 X X 0 0 X 0 X X X X X X X 0 0 0 0 0 0 X X X X 0 0 X 0 X 0 X 0 0 X X 0 X X X X X 0 0 X 0 0 0 0 X 0 X X 0 X generates a code of length 79 over Z2[X]/(X^2) who´s minimum homogenous weight is 68. Homogenous weight enumerator: w(x)=1x^0+131x^68+248x^70+400x^72+386x^74+538x^76+416x^78+484x^80+396x^82+372x^84+240x^86+257x^88+98x^90+83x^92+8x^94+25x^96+11x^100+1x^104+1x^108 The gray image is a linear code over GF(2) with n=158, k=12 and d=68. This code was found by Heurico 1.16 in 3.48 seconds.