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 X X 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 0 X 0 X 0 X 0 X X X X X X^2 X 0 X X 1 0 X 0 X^2+X 0 X^2+X 0 X 0 X^2+X 0 X 0 X^2+X 0 X 0 X^2+X 0 X 0 X^2+X 0 X X^2 X^2+X X^2 X X^2 X^2+X X^2 X X^2 X^2 0 X^2+X X^2 X X^2 X^2+X X^2 X 0 X^2+X X^2 X X^2 X^2+X X^2 X 0 X^2+X X^2 X^2+X 0 X X^2 X^2+X X X^2 X^2 X X^2 X^2+X X^2 X X^2+X X X^2+X X X^2+X X X^2+X X 0 X^2+X X^2+X X X 0 X X X^2+X X^2+X 0 0 0 X^2 0 0 0 X^2 0 0 0 0 0 X^2 0 X^2 0 0 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 0 0 X^2 0 X^2 X^2 0 0 X^2 0 X^2 X^2 0 X^2 0 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 0 0 0 0 0 0 X^2 X^2 0 X^2 X^2 0 0 0 X^2 X^2 X^2 0 X^2 X^2 0 0 0 0 0 X^2 0 0 0 X^2 0 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 0 0 0 X^2 0 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0 0 0 0 X^2 0 X^2 X^2 X^2 0 X^2 0 0 0 0 X^2 0 X^2 0 X^2 0 0 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 0 0 0 0 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 0 0 X^2 0 0 0 0 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 0 X^2 0 0 X^2 0 0 X^2 0 0 X^2 X^2 0 0 0 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 0 0 X^2 0 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 0 0 0 0 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 0 X^2 X^2 X^2 0 0 X^2 X^2 0 0 0 0 0 0 X^2 0 0 X^2 X^2 0 X^2 0 X^2 0 0 X^2 X^2 X^2 0 generates a code of length 85 over Z2[X]/(X^3) who´s minimum homogenous weight is 80. Homogenous weight enumerator: w(x)=1x^0+7x^80+68x^81+26x^82+84x^83+34x^84+92x^85+26x^86+88x^87+18x^88+28x^89+8x^90+20x^91+2x^92+4x^93+2x^94+2x^96+1x^98+1x^130 The gray image is a linear code over GF(2) with n=340, k=9 and d=160. This code was found by Heurico 1.16 in 0.46 seconds.