The generator matrix 1 0 1 1 1 X^2+X 1 1 0 X^2+X 1 1 1 X^2 1 1 X 1 1 1 X^2 1 0 1 1 1 X^2 X^2 X^2 1 1 1 1 1 1 X X 1 1 1 1 X^2+X 1 1 1 1 1 1 1 0 X^2+X 1 1 X X^2+X X 1 1 X X 1 1 X^2+X 1 1 1 1 X X^2 1 1 0 1 1 0 1 1 X X^2+X+1 1 1 X^2+X+1 X^2+X 1 1 0 X 1 X^2+1 X^2 X+1 1 X^2+X 1 X+1 1 X 1 1 1 0 X+1 X X^2 X^2+X 1 1 1 1 1 X^2+X X^2+X 1 X^2+X+1 X^2+1 X^2+X+1 0 X^2+X+1 X^2+X+1 X^2+1 1 1 X^2+X+1 X^2+1 1 1 X X^2+X+1 X^2+X 1 0 1 X 1 X^2+X+1 X^2+X+1 1 X^2+X 1 1 X^2 0 0 0 X 0 0 0 0 0 0 X^2 0 0 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2+X X^2+X X^2+X X X^2+X X^2+X X X^2+X X X X X X X^2+X X^2+X X^2 X^2 X X^2+X 0 X 0 0 X X X^2+X X^2 X X^2 X^2+X 0 X X X X^2 0 X 0 X X^2 0 0 X^2+X X^2 X^2+X 0 X 0 0 0 0 X 0 0 X X^2 X X^2+X X X^2 X^2+X X X X^2 0 X 0 0 X^2+X X X^2 X X^2+X X X^2 X 0 X^2+X X^2 X X^2+X 0 X^2 X X X^2+X X X^2 X^2 X^2 0 X X^2+X X X^2 X^2+X X^2+X X^2 X^2 X X^2 0 0 0 0 0 X X^2 X 0 X X^2 X X^2 X X^2+X X^2 0 0 0 0 0 0 X 0 0 X X X^2+X X^2 X^2 X^2 X^2 X^2+X X^2+X X X^2+X X X^2 0 X^2+X X 0 X X^2+X 0 X X^2+X X^2 X^2+X 0 X^2+X 0 0 X^2 X X^2 X X X^2+X 0 X^2+X X^2+X X X X^2+X 0 X 0 X^2+X 0 X^2+X X^2+X X^2 X^2 X^2 X^2+X 0 X X^2 X^2 0 0 X X^2 X^2 X^2 X X^2 0 0 0 0 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 0 X^2 0 X^2 0 0 X^2 X^2 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 0 generates a code of length 71 over Z2[X]/(X^3) who´s minimum homogenous weight is 62. Homogenous weight enumerator: w(x)=1x^0+59x^62+132x^63+213x^64+356x^65+499x^66+568x^67+619x^68+710x^69+708x^70+704x^71+680x^72+652x^73+607x^74+498x^75+413x^76+270x^77+171x^78+110x^79+67x^80+54x^81+30x^82+30x^83+11x^84+4x^85+5x^86+6x^87+10x^88+2x^89+1x^92+1x^94+1x^96 The gray image is a linear code over GF(2) with n=284, k=13 and d=124. This code was found by Heurico 1.16 in 4.89 seconds.