The generator matrix 1 0 1 1 1 0 1 1 0 1 1 X 1 1 0 1 0 1 1 1 X 1 1 0 1 0 1 1 0 1 1 1 1 0 X 1 1 1 0 0 X 1 1 1 1 1 1 1 1 X 1 1 X 1 1 X 1 1 0 1 X 1 1 1 1 X 0 1 1 0 X X 1 1 1 X X X 0 X 0 1 1 0 1 1 0 1 1 0 X+1 1 X X+1 1 0 1 X+1 X X+1 1 X+1 0 1 X 1 X+1 0 1 X+1 X+1 0 0 1 1 0 X+1 X 1 1 1 0 1 X+1 X+1 1 0 X+1 0 1 0 1 1 1 1 1 1 X+1 1 0 1 X X 0 1 1 1 0 X+1 1 1 1 X+1 X+1 X+1 1 X 1 1 1 0 0 X 0 0 0 0 0 0 0 X 0 0 0 0 0 X X 0 X X X X X X 0 X 0 0 0 X X X X 0 X 0 0 0 X X 0 0 X X 0 0 0 0 0 X 0 0 X X 0 0 X X 0 X 0 0 0 X X X 0 0 X 0 0 X X 0 0 X X X X 0 0 0 X 0 0 0 0 0 0 0 0 X 0 0 0 0 X X X 0 X 0 0 0 0 X X X 0 X X X 0 0 0 X X 0 0 0 0 X 0 X 0 X 0 0 X X 0 X X 0 X X 0 X 0 X X X X 0 0 0 X X X X 0 X X 0 X 0 X X X 0 0 0 0 X 0 0 0 0 0 X 0 0 0 X 0 X X 0 X 0 0 X 0 X X 0 0 X X X 0 0 X X 0 0 X 0 0 0 X X X X 0 0 X 0 0 X 0 X 0 0 0 X X X 0 X 0 X X X 0 0 X 0 X 0 X X 0 X X X X X 0 0 0 0 0 0 X 0 0 0 0 0 X 0 0 0 0 0 0 0 0 0 0 X X X X X X X X X X 0 X 0 X X 0 0 X X X X 0 X X 0 X X 0 X 0 0 0 X X X 0 X X X 0 0 0 X 0 0 X 0 X X 0 0 X X 0 0 0 X X 0 0 0 0 0 0 X 0 0 0 0 0 0 X 0 0 X 0 X X X X 0 X X X 0 X 0 0 0 0 X X 0 0 0 0 X X X X X 0 X 0 X X 0 0 0 X 0 X 0 X X X X 0 0 X 0 X X 0 X 0 0 0 X 0 0 X 0 0 0 X 0 0 0 0 0 0 0 0 0 X 0 0 X 0 0 0 X X X 0 X X 0 0 X 0 0 0 X X 0 X X 0 X 0 0 X X 0 0 X X X X 0 0 X 0 0 0 X X X X 0 0 X X X X 0 X 0 0 0 0 X X X X 0 0 X X X 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X 0 0 X 0 X X 0 X X 0 0 0 X 0 0 0 X X X 0 X 0 0 X X X X 0 0 0 0 X X 0 X 0 X 0 0 X X X 0 0 X X X X 0 X 0 X X X X 0 0 X 0 0 X 0 0 0 0 X X X 0 0 0 0 0 0 0 0 0 0 0 0 X 0 0 X X X X 0 0 X X X X X 0 X 0 0 0 0 0 0 0 X X X X X 0 0 X 0 X 0 X X 0 X 0 X X X 0 X 0 X 0 X 0 X 0 0 0 0 X 0 0 0 X 0 X X X 0 X X 0 0 0 0 X generates a code of length 80 over Z2[X]/(X^2) who´s minimum homogenous weight is 68. Homogenous weight enumerator: w(x)=1x^0+117x^68+90x^70+393x^72+284x^74+555x^76+412x^78+548x^80+352x^82+470x^84+314x^86+299x^88+84x^90+104x^92+46x^96+17x^100+8x^104+1x^108+1x^112 The gray image is a linear code over GF(2) with n=160, k=12 and d=68. This code was found by Heurico 1.16 in 4.22 seconds.