The generator matrix 1 0 0 0 0 1 1 1 0 1 1 X 1 0 1 0 0 1 X 1 1 X 0 X 1 X 1 1 X X 1 1 1 1 1 0 X X 0 X X 1 X 0 1 1 X 1 X 1 X X 1 1 1 X 0 1 0 X X 1 1 1 0 1 1 1 1 X 1 0 X 0 0 X 1 1 1 1 0 1 0 0 0 0 0 0 0 1 1 1 1 1 X+1 X 1 1 1 1 X 0 1 0 X 1 0 X+1 0 X 1 X+1 X 0 X 1 1 1 0 1 1 X+1 1 X 0 X+1 1 X 1 X+1 1 1 0 X+1 X+1 X 1 X 1 X 1 X+1 1 0 1 0 0 X+1 X+1 1 1 1 1 X X 1 1 X+1 0 X 0 0 1 0 0 0 1 1 1 1 X+1 0 0 X+1 X 0 X+1 1 X X+1 0 1 X 1 0 X+1 X+1 0 1 1 1 X+1 0 1 0 X 0 X X 1 1 X+1 1 1 1 1 X+1 0 1 0 0 X+1 X+1 X+1 0 1 0 X X 1 X 0 X X X X 1 X+1 X X+1 X+1 1 0 X 1 X X+1 0 1 1 0 0 0 1 0 1 1 0 1 X X+1 1 0 1 1 X X X X+1 1 1 X+1 X X 0 0 1 0 1 0 0 1 0 0 X+1 1 0 X+1 1 X 0 X+1 1 0 X+1 X+1 X X 1 X X 0 X+1 X+1 1 1 1 X X X+1 1 1 1 0 1 X X X+1 1 X X 1 X 1 0 X 0 X+1 X 1 0 0 0 0 1 1 0 1 X+1 X X+1 X+1 1 X 0 1 1 0 X+1 1 X+1 1 X 0 0 1 X+1 1 X 1 1 X X+1 1 X X X+1 0 X+1 0 0 1 X X+1 X X 1 X 1 X 1 1 1 X+1 X+1 1 X X 0 X+1 0 X+1 X+1 X X 1 X 0 0 0 0 X 1 0 X 1 1 X+1 X+1 1 0 0 0 0 0 X 0 0 X 0 X X X X 0 X 0 X 0 0 0 0 X X X X X X 0 X X 0 0 X 0 X 0 0 0 0 X X X X X X X X 0 X X 0 0 X X 0 0 X 0 X 0 X 0 0 X 0 X 0 X 0 X 0 X 0 0 X X 0 X 0 0 0 0 0 0 0 X 0 0 0 0 0 X 0 0 X X X X 0 0 X 0 0 X 0 X 0 X X 0 0 X X 0 0 X 0 0 X X 0 X X 0 X 0 0 0 X X X 0 X X X X 0 0 0 X 0 X X X 0 0 X X X X 0 X X X 0 0 0 X 0 0 0 0 0 0 0 0 X 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X X X X X X X X X X X X X X X X X 0 X 0 X X X 0 0 X X X X 0 X X X 0 0 0 0 X 0 X X X 0 X X 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+155x^68+426x^70+668x^72+759x^74+810x^76+858x^78+985x^80+844x^82+834x^84+662x^86+502x^88+324x^90+230x^92+86x^94+28x^96+8x^98+11x^100+1x^106 The gray image is a linear code over GF(2) with n=160, k=13 and d=68. This code was found by Heurico 1.16 in 13.1 seconds.