The generator matrix 1 0 1 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 X 1 1 0 1 1 1 X 1 1 0 1 0 1 0 1 1 1 1 X 1 1 1 0 1 1 1 X X 1 1 1 1 1 1 1 0 1 X X 1 X 0 0 1 1 0 1 1 1 1 1 X 0 0 X 1 X 0 0 X 1 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 X+1 1 0 X+1 1 0 X+1 1 X+1 0 1 X+1 0 1 1 0 0 1 X X+1 1 X+1 1 X+1 1 0 X 1 1 1 X X+1 0 1 X+1 X 1 1 1 X X+1 X+1 1 0 0 0 1 X 1 1 1 1 1 1 X X+1 1 0 X 0 X+1 0 X X 0 1 1 0 0 X 0 0 0 0 0 0 X 0 0 0 0 0 0 0 0 0 0 0 0 X 0 0 0 0 X X X X X X 0 X 0 X 0 0 X 0 X X X 0 X X 0 X X 0 0 X 0 0 0 0 X 0 X X 0 0 X X X X X X 0 0 X X X X X 0 0 0 0 0 0 X X X 0 0 X 0 0 X 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 0 0 0 0 0 0 X X X X X X X X X X X X X X 0 X X X X X 0 X X 0 0 X X X 0 X X X X X X X X X X X 0 X X X 0 X X 0 X 0 0 0 0 0 0 0 X 0 0 0 0 0 0 0 0 0 X 0 0 0 X X X X X 0 X X 0 0 X X 0 X X 0 0 X X X 0 0 0 0 0 0 0 X X 0 X X X 0 X 0 X 0 0 0 0 X X 0 0 X 0 X X X 0 0 0 X 0 0 X 0 X 0 X 0 X 0 X X 0 0 0 0 0 0 0 0 X 0 0 0 0 0 0 0 0 0 X 0 0 0 0 X X X X X 0 X 0 X 0 X X 0 X X X X X 0 X 0 0 0 X X 0 0 0 0 0 0 0 0 0 X X X 0 0 X X X 0 X X 0 X X X X 0 X 0 X X 0 0 0 X 0 0 0 0 X 0 0 0 0 0 0 0 0 0 X 0 0 0 0 0 0 0 X 0 X X X X X X 0 X X 0 0 X X X X X 0 X 0 X 0 0 0 X X X X 0 X X 0 X X 0 X X 0 X X X 0 0 0 X X X 0 0 0 0 X 0 X X X 0 0 X 0 0 X 0 0 X X X 0 0 0 0 0 0 0 0 0 0 0 0 X 0 0 0 0 X 0 0 0 X X X 0 0 X X X X X X X 0 X 0 X 0 0 0 0 0 X X 0 X X 0 0 0 X X 0 0 X 0 X X X X 0 X 0 0 0 0 0 X X 0 0 X X 0 X X X X X 0 X 0 X X X X X X 0 0 0 0 0 0 0 0 0 0 0 0 X 0 0 0 X 0 0 0 0 X X X 0 X X 0 X X X X X 0 0 0 X X X X X 0 0 X X X 0 0 X X X X 0 0 X 0 0 X X X X X 0 0 0 X X 0 X 0 0 0 0 X X X 0 X X X X 0 X 0 X 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X 0 0 0 X 0 0 0 X X 0 0 0 0 X X X 0 0 X X X 0 X 0 X 0 X X X X 0 X 0 X 0 0 X 0 0 X X X 0 X X X X 0 X X 0 X X 0 0 X 0 0 0 X X 0 0 X X 0 X X 0 X 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X 0 X X X X 0 X 0 0 0 0 X 0 0 X X X X X 0 0 X 0 0 0 X 0 0 X 0 X X 0 X X 0 X X X 0 X X 0 0 0 X 0 0 X X 0 0 0 0 X X 0 X X 0 0 0 X X 0 X X X X X X X 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X X X X X X X X 0 X 0 X 0 X 0 0 0 0 X X 0 X 0 0 0 0 0 0 X X X 0 0 0 0 X X 0 0 X 0 X 0 X X 0 0 0 X 0 0 X 0 X 0 X 0 0 X 0 X X 0 X 0 X X 0 X X 0 0 X X X 0 generates a code of length 87 over Z2[X]/(X^2) who´s minimum homogenous weight is 68. Homogenous weight enumerator: w(x)=1x^0+76x^68+69x^70+22x^71+212x^72+54x^73+224x^74+144x^75+398x^76+264x^77+392x^78+412x^79+554x^80+664x^81+608x^82+878x^83+742x^84+1058x^85+764x^86+1146x^87+814x^88+1098x^89+814x^90+924x^91+695x^92+636x^93+553x^94+424x^95+355x^96+260x^97+356x^98+134x^99+183x^100+58x^101+219x^102+12x^103+46x^104+4x^105+70x^106+15x^108+18x^110+2x^112+8x^114+3x^116+1x^126 The gray image is a linear code over GF(2) with n=174, k=14 and d=68. This code was found by Heurico 1.16 in 65.5 seconds.