The generator matrix 1 0 0 0 0 0 1 1 1 X 0 0 0 0 1 1 1 0 X 1 1 X 1 X 1 1 1 1 0 X X 1 1 1 1 1 1 1 0 1 1 0 0 X X 1 X 1 X 1 X 1 X 1 1 1 1 1 1 0 0 1 X 1 1 X 0 1 1 X 1 1 1 X 1 1 X 0 1 0 0 0 0 0 0 0 0 1 X 1 1 0 X 1 X 0 1 X 1 X 1 1 1 1 X 1 1 X 0 X X+1 0 X X+1 X+1 1 X+1 X+1 1 1 0 1 1 1 1 0 X+1 1 0 1 1 X 1 0 X+1 X 1 1 X+1 X 0 0 1 1 X+1 X 0 1 1 X 1 0 0 X 0 0 1 0 0 0 0 0 0 0 X 1 1 X+1 X+1 X+1 X 1 1 X+1 0 0 X 1 0 X+1 1 X+1 1 0 0 X+1 X+1 1 X X+1 X 0 0 X+1 1 X 1 1 0 X 1 0 X X+1 X X+1 1 X 0 X+1 X 1 X X 0 1 1 1 X 1 X 0 X 1 X+1 1 0 X X X+1 1 0 0 0 1 0 0 0 1 1 1 X+1 X+1 1 X 0 X+1 0 1 X X+1 X X+1 X+1 1 1 0 X 1 0 0 1 X X X+1 X X 1 X 0 X+1 X+1 X+1 X+1 X X 0 X 0 0 X+1 1 X+1 0 X+1 0 0 1 X X X X+1 1 X 0 1 0 X+1 0 1 X 1 X X+1 1 X 0 X 0 0 0 0 1 0 1 1 X X+1 1 1 1 0 X+1 0 1 0 1 0 X X X+1 0 X+1 X+1 X 1 X+1 1 0 0 X+1 X+1 X+1 X X 1 1 0 1 1 1 X 1 0 0 X+1 1 X X 0 0 X 1 1 0 X+1 0 X 1 1 X X+1 X+1 X+1 X+1 X X+1 X+1 0 X 1 1 1 X 0 0 0 0 0 0 1 1 X X+1 1 0 X 1 X+1 0 X X X+1 1 X+1 0 X+1 0 0 1 1 0 1 X X+1 0 X+1 0 X 1 1 X 0 X+1 1 X 0 X+1 0 X 0 0 X+1 X+1 X 0 1 X+1 1 X X X X 0 X 1 1 1 1 0 X+1 1 X+1 1 1 0 X 0 1 1 X+1 X+1 0 0 0 0 0 0 X 0 X 0 0 0 0 0 X X X 0 0 X X 0 X 0 X 0 0 0 X X X 0 0 0 0 X X 0 0 0 X X X X X 0 X X 0 0 0 X X X X 0 X X 0 X X X X 0 X 0 0 0 0 X X 0 0 X X 0 0 generates a code of length 77 over Z2[X]/(X^2) who´s minimum homogenous weight is 65. Homogenous weight enumerator: w(x)=1x^0+68x^65+113x^66+230x^67+320x^68+310x^69+352x^70+364x^71+414x^72+450x^73+442x^74+440x^75+431x^76+456x^77+457x^78+462x^79+409x^80+364x^81+401x^82+350x^83+342x^84+282x^85+220x^86+160x^87+102x^88+94x^89+58x^90+36x^91+26x^92+24x^93+3x^94+6x^95+2x^96+2x^98+1x^108 The gray image is a linear code over GF(2) with n=154, k=13 and d=65. This code was found by Heurico 1.16 in 12.3 seconds.