The generator matrix 1 0 0 1 1 1 0 1 1 1 1 0 X X 1 1 1 1 X X 0 1 1 X 1 0 0 1 1 X 1 1 1 X 1 X X 0 1 1 1 1 1 X 1 X 1 1 1 X X 1 X 0 X 1 0 0 X X 0 X 1 X 1 X X 0 1 0 1 1 1 X 1 X 1 0 X 1 1 X 1 0 1 1 0 1 0 1 0 1 1 0 0 1 X+1 1 X 1 0 X X+1 1 1 1 0 X+1 0 1 0 1 0 X+1 1 X X 0 X+1 1 X 0 0 1 X+1 1 0 0 1 1 X 1 0 X X 1 1 X 0 X 0 0 X 1 1 1 0 0 1 1 1 1 1 1 1 1 1 0 X+1 1 X 1 X X 1 X 1 1 1 1 X+1 0 0 0 1 1 1 0 1 0 1 1 0 X 1 X+1 X+1 X 0 X+1 X X+1 1 X+1 X X+1 X+1 X 1 0 0 1 1 0 1 1 1 1 1 X X+1 X+1 X 0 X 1 X+1 X X+1 X 0 X+1 1 0 1 1 1 X+1 1 0 1 0 1 1 X+1 X 0 X X 0 0 X+1 X X+1 X 1 0 1 0 1 0 X 1 X+1 1 X X+1 0 0 0 0 X 0 0 0 0 0 0 0 0 0 X X X X X 0 X 0 0 0 0 X 0 0 X X X 0 X 0 0 X 0 X X X 0 X 0 X X 0 X 0 X X 0 0 X X X X X X 0 X 0 0 X 0 X 0 0 X X X X 0 0 0 0 0 0 X 0 X X X 0 X 0 0 0 0 0 0 0 X 0 0 0 0 0 X X X 0 X X 0 0 0 X X 0 0 X 0 X X 0 X 0 X 0 X X X X 0 0 0 X X X X 0 0 0 0 0 X X 0 0 0 0 X 0 0 X X 0 X X 0 X 0 X X X X 0 X 0 0 0 0 X 0 X 0 0 X 0 0 X 0 0 0 0 0 0 0 X 0 0 0 0 X 0 0 0 0 0 X 0 0 0 X X X X X X X 0 X X X X 0 0 X 0 0 X 0 0 0 X 0 X X 0 0 X X X 0 0 0 X X 0 0 0 0 X 0 X X X X 0 0 0 X 0 X 0 0 X 0 X X X 0 0 0 X X X 0 0 0 0 0 0 0 0 X 0 0 0 0 0 0 X 0 0 0 0 0 X 0 0 0 X 0 0 X 0 0 X 0 X X X X X X 0 0 0 X 0 0 X X 0 X X X 0 X X 0 X 0 X 0 0 0 X X 0 0 X X X 0 X X X X 0 0 0 0 X X X X 0 X 0 0 0 0 0 0 0 0 0 0 0 0 X 0 0 0 0 0 0 0 0 0 X X X X X X X 0 X 0 X 0 X X X 0 X 0 X 0 X 0 0 X 0 X X X X X 0 0 X X 0 0 X X 0 0 X X 0 X X 0 0 0 0 0 X X X X X X X 0 0 0 X 0 X 0 0 X 0 0 0 0 0 0 0 0 0 0 0 X 0 X X X 0 0 X 0 0 0 X X 0 0 X X X 0 0 X 0 0 0 X 0 0 0 X X X 0 0 0 0 X X X X 0 0 0 0 X X 0 0 X 0 X X 0 X X X 0 X X X 0 X X 0 0 X X 0 X X 0 0 0 X 0 X 0 0 0 0 0 0 0 0 0 0 0 0 X 0 0 0 X X X X 0 0 X X 0 X X 0 X 0 X 0 0 0 0 X X 0 0 X 0 0 X 0 0 X X 0 X X 0 X 0 X X X X X 0 0 X 0 0 0 X X 0 0 X X X 0 0 0 0 0 X X X X X X X 0 0 0 X X X generates a code of length 86 over Z2[X]/(X^2) who´s minimum homogenous weight is 72. Homogenous weight enumerator: w(x)=1x^0+57x^72+42x^73+101x^74+122x^75+256x^76+258x^77+308x^78+300x^79+380x^80+356x^81+377x^82+446x^83+387x^84+536x^85+449x^86+498x^87+399x^88+452x^89+363x^90+398x^91+340x^92+298x^93+274x^94+232x^95+161x^96+92x^97+101x^98+42x^99+51x^100+12x^101+50x^102+10x^103+10x^104+2x^105+16x^106+6x^108+6x^110+2x^114+1x^118 The gray image is a linear code over GF(2) with n=172, k=13 and d=72. This code was found by Heurico 1.16 in 15.8 seconds.