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 1 X^2 X 0 X X^2 1 X 1 X 1 0 1 X 0 1 1 1 1 1 1 X X X X X^2 X X^2 1 X 1 1 1 1 1 X X 1 X 1 1 X 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 X 0 X^2+X X^2 X X^2 X^2+X X^2+X X X^2 X^2+X X^2+X X^2 X 0 X^2+X X^2+X X X X 0 X X X 0 X 0 X^2+X X X^2 0 X^2+X X X X 0 X^2+X X^2 0 X 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^2+X 0 X^2 X X 0 0 X^2 X^2 X X X^2+X X^2 X 0 0 X^2+X X^2+X X^2+X X^2+X 0 X^2 X X X^2 X^2 X X^2+X X X^2+X 0 0 X^2 X^2+X X^2+X X^2 0 0 X 0 X 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 X^2+X X X^2+X X^2 X^2 X X^2 X 0 0 0 0 0 X^2 X^2 X^2+X X^2+X X^2+X 0 X^2+X X 0 X X^2+X X^2+X 0 X^2+X 0 X^2 X^2+X X X 0 X^2+X 0 X X^2 0 X^2+X X^2+X 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^2+X X^2+X X X^2+X X^2+X X^2 X^2 X^2 X^2+X 0 0 X^2 X^2+X X X^2+X X^2 X X^2+X X^2 X^2 X^2 X^2 X^2 X^2 X^2+X X^2+X X^2+X X X^2 X X^2+X X^2+X X^2+X X^2 X^2+X 0 X^2 X^2+X 0 X 0 X^2+X 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 0 0 X X X^2+X X^2+X 0 0 X^2+X X^2 X^2+X 0 X^2+X X^2 X^2 X^2 X^2 0 X^2+X 0 X X^2 X^2+X 0 X^2 X^2+X X^2 0 X X^2+X X^2+X 0 X 0 0 X X^2 X^2 0 X^2 X^2+X 0 generates a code of length 80 over Z2[X]/(X^3) who´s minimum homogenous weight is 70. Homogenous weight enumerator: w(x)=1x^0+218x^70+4x^71+373x^72+40x^73+588x^74+184x^75+708x^76+380x^77+838x^78+420x^79+880x^80+452x^81+842x^82+356x^83+605x^84+132x^85+434x^86+56x^87+295x^88+20x^89+176x^90+4x^91+118x^92+38x^94+27x^96+2x^98+1x^116 The gray image is a linear code over GF(2) with n=320, k=13 and d=140. This code was found by Heurico 1.16 in 28.8 seconds.