The generator matrix 1 0 0 1 1 1 X 1 X^2+X 1 1 X 1 X^2 1 1 X X 1 1 1 X^2+X 1 X^2+X X^2 1 1 0 1 1 1 X X^2 1 X 1 1 1 X^2+X X 1 X 1 X^2+X 1 X^2+X 1 X 0 0 1 1 1 X^2+X 1 1 X^2+X X^2 X X X^2+X X^2+X 1 X 1 1 1 1 1 1 X^2+X 1 1 1 1 1 1 1 1 1 0 1 0 0 1 X^2+X+1 1 X^2 0 X^2 X^2+X+1 1 1 1 X^2 X+1 X^2+X 1 X X^2+X+1 X^2 1 X^2+X+1 X^2+X 1 X^2+X+1 X 1 1 X^2+X X^2+1 1 0 X^2+X+1 1 X 1 X^2+X 1 1 X^2+X 1 X^2 1 0 0 1 1 X^2+X 1 0 X^2+1 X^2+X 1 X^2 X^2+1 X^2+X 1 1 1 1 X^2 X^2 X^2 X 1 1 0 0 X^2+X 1 0 1 X^2+X+1 X^2+1 X+1 1 X^2+X X+1 X^2 0 0 1 1 X+1 0 1 X+1 1 X X+1 X 0 1 0 1 1 X^2 X^2+X X 1 X^2+X+1 X^2 1 0 1 X^2+1 X+1 0 X^2 X^2+X+1 1 1 X^2 0 X+1 X+1 0 X^2+X X^2+X+1 X^2+X X X^2+1 X^2+X+1 X^2+X 1 X^2+X X+1 1 0 X^2+1 0 X X^2+1 X^2+1 X+1 1 1 X X^2+X X^2 1 X^2+X 1 X^2 X^2+X+1 X X^2+X 1 X 0 X+1 X X^2+X+1 X^2+X X^2+X+1 X^2+X X^2+1 X X^2+X 0 0 0 X X X^2+X X^2 X^2+X 0 0 X X^2 X^2+X 0 X X X^2 0 0 X^2+X X^2 X^2+X X^2 X X^2+X X^2 0 X 0 X^2+X 0 X X^2+X X^2 X 0 X X^2+X 0 X X X^2+X X^2 0 X^2+X X^2 X X^2 X^2+X X^2 0 0 0 X X X^2 X X^2+X X^2+X X 0 X^2+X X^2 X^2 0 0 X^2+X X^2 X 0 0 0 X^2 X^2+X X^2+X X^2 X^2+X X^2 X^2 X^2 0 0 0 0 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 0 0 0 0 0 X^2 0 X^2 0 0 X^2 0 X^2 0 X^2 0 0 0 0 0 0 X^2 0 X^2 0 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 0 0 0 0 0 0 0 X^2 X^2 0 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 0 0 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 0 0 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 generates a code of length 80 over Z2[X]/(X^3) who´s minimum homogenous weight is 72. Homogenous weight enumerator: w(x)=1x^0+93x^72+318x^73+453x^74+496x^75+591x^76+654x^77+696x^78+698x^79+644x^80+646x^81+548x^82+538x^83+498x^84+336x^85+336x^86+260x^87+141x^88+84x^89+61x^90+36x^91+15x^92+8x^93+16x^94+18x^95+1x^96+2x^98+2x^99+2x^101 The gray image is a linear code over GF(2) with n=320, k=13 and d=144. This code was found by Heurico 1.16 in 4.13 seconds.