The generator matrix 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X^2 X X X X^2 1 0 1 X^2 1 0 X^2 0 1 1 1 0 X 1 1 1 X X X X^2 X^2 1 X^2 1 X 1 0 1 1 1 0 0 1 X^2 X 1 0 X 0 0 0 0 0 0 X^2 X^2 X X^2+X X 0 0 X^2 X^2+X X^2+X X X X X 0 X X^2+X X 0 X X^2+X X^2 X^2+X X^2 X^2 X^2+X X 0 0 X X^2 X^2 X^2+X X^2 X X X^2 X X X X^2 0 X^2 X^2+X 0 X X X X X^2 X^2 X X X^2+X X X 0 X X X X^2 X^2 X^2 X^2+X X^2 X X X X^2 X^2 0 0 0 X 0 0 0 0 0 0 0 0 0 X^2 X^2+X X^2+X X^2+X X X^2+X X^2+X X X^2 X^2 X^2+X X^2+X 0 0 X X X X^2+X X^2+X X^2+X X^2 X^2 X^2+X X X X^2 X^2 X X 0 X X^2 X 0 X^2+X 0 0 X X^2 X^2+X X^2 X^2+X X 0 X^2+X 0 X^2 0 0 X^2 X X^2 X X X^2 X X^2 X X^2+X X^2+X 0 X^2 X^2+X X X^2 0 0 0 0 0 X 0 0 X^2 X^2+X X X X X X^2 X^2+X X X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X X^2+X X X^2 X X^2+X X^2+X X X^2+X 0 X^2 0 0 0 X^2+X X^2 X X^2+X 0 0 0 X 0 X X^2 X X X X 0 0 X X^2 X^2 0 X^2 0 X^2+X 0 X^2+X X^2 0 X^2+X X^2+X 0 0 0 X 0 X X^2+X X 0 X X 0 0 0 0 0 X 0 X^2+X X^2+X X X^2 X^2+X X^2+X 0 X X 0 X^2 X 0 X^2+X X^2+X X X^2+X X X^2 X^2 X X^2 X^2 0 X^2+X X^2 0 X^2+X X X^2+X X^2 0 X 0 0 X^2 0 X 0 X 0 X^2 0 X X^2+X X^2+X X^2+X X^2+X X 0 X^2 0 X^2 0 X X^2 X X^2+X 0 0 X^2+X X X^2 X^2 0 X^2 X^2+X X^2 0 0 X^2 0 0 0 0 0 0 0 X X X^2 X^2+X X X^2+X X^2 X X 0 X 0 X^2+X X^2+X 0 X X^2 X^2 X^2+X X^2 X X^2+X X^2+X X^2 X X^2 X^2 X^2+X 0 X X^2+X 0 0 X X 0 X^2+X X^2 X^2 X^2 X^2+X X X^2+X X^2 X X^2 X X^2 X^2 X X X^2+X X 0 X^2 X X X^2+X X^2+X X 0 X 0 X^2 0 X^2 X^2+X X X^2+X X^2+X 0 X^2+X 0 0 generates a code of length 79 over Z2[X]/(X^3) who�s minimum homogenous weight is 68. Homogenous weight enumerator: w(x)=1x^0+55x^68+102x^69+164x^70+218x^71+257x^72+310x^73+407x^74+542x^75+568x^76+604x^77+669x^78+668x^79+627x^80+602x^81+515x^82+412x^83+361x^84+316x^85+202x^86+136x^87+125x^88+88x^89+75x^90+60x^91+40x^92+26x^93+12x^94+10x^95+14x^96+3x^98+2x^99+1x^110 The gray image is a linear code over GF(2) with n=316, k=13 and d=136. This code was found by Heurico 1.16 in 7.12 seconds.