The generator matrix 1 0 0 0 0 1 1 1 0 1 X^2 1 X^2 1 X^2+X 1 0 1 1 X 1 X^2+X X 1 X X^2+X X 1 1 1 1 X^2+X 1 X^2 1 X^2+X 1 1 1 1 X^2 X^2+X 0 1 X 1 X^2 1 X^2+X 1 X^2 X^2 X 1 1 X X^2+X 1 1 X 1 1 X^2+X 1 0 X^2+X X X^2 0 X X^2+X 1 X^2 X^2+X 1 X^2 X^2 1 X^2 1 0 1 0 0 0 0 0 X^2 X^2 1 1 1 1 1 1 X+1 X^2+X X^2+X+1 X^2+X X X+1 1 1 X^2 1 1 0 X^2+X X 1 X^2 1 X^2+1 0 X^2+1 X^2 X X^2+X 1 X+1 1 X^2 1 0 X X^2+X+1 X^2+X X^2+X+1 1 X+1 0 1 1 X^2+X X+1 1 1 X X^2+X+1 1 1 0 X^2 X^2+1 1 X^2+X 1 X^2 1 1 1 X X^2+X X^2+X X+1 X^2+X 1 X+1 1 0 0 0 1 0 0 X^2 1 X^2+1 1 0 1 X+1 X^2+X+1 X^2+1 0 X 1 X X^2+X+1 1 X+1 0 X X X^2+1 X^2+1 X^2+X X^2 1 0 X^2+1 X X+1 X^2+X X^2+X+1 1 X^2 X^2 X X^2+1 0 X^2 X^2+X+1 X^2+X+1 X X^2+X 1 X^2+X+1 1 X^2+X+1 X 0 1 0 X+1 X^2+X+1 X 0 X^2+X+1 X^2 X^2 1 1 X^2+X+1 X+1 0 X+1 1 X^2+X X^2+X X^2+1 X+1 1 X X^2+1 0 X^2+X+1 X^2 1 0 0 0 0 1 0 X^2+1 1 0 1 X^2 X^2+1 X+1 X^2 X^2+X X^2+1 X^2+X+1 X^2+X 1 0 X^2+X+1 X^2+1 X^2+X X+1 0 X^2+X+1 0 1 X^2+1 1 0 X X^2+X X 1 X^2 X^2 X+1 X^2+X X^2 X+1 X^2+1 1 X+1 X^2+X 0 X+1 X 1 X^2 0 1 0 X^2+1 X+1 X^2+X+1 X 1 X^2+1 X X^2 X^2+X+1 1 X^2+X X X^2 1 X^2+1 X^2+X+1 0 X^2+X X^2+X X^2+1 X^2+X+1 1 1 X 0 X^2+X+1 X^2 X^2 0 0 0 0 1 1 X^2 1 1 X^2+1 X^2 1 X+1 0 1 0 X^2+1 X+1 X^2+X X^2+X X^2+X X^2+X+1 0 X^2+X+1 X^2+1 X X+1 X^2 1 X X X^2+X X+1 0 X^2 X+1 X+1 X^2+X+1 0 1 X 1 X^2+X 1 1 1 0 X^2 0 X^2 X X+1 X^2+1 X^2+X X^2+X X^2 X^2+X+1 X X^2+X+1 0 X^2 X^2+X X^2+X X^2+1 1 X^2+X+1 X^2+1 X X^2 X^2+1 0 1 X^2 X^2 X 1 X^2+X X^2 X^2+X+1 X^2 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+82x^70+474x^71+696x^72+1338x^73+1240x^74+2044x^75+1768x^76+2496x^77+2152x^78+2858x^79+2529x^80+2896x^81+2196x^82+2788x^83+1744x^84+1886x^85+1132x^86+1008x^87+510x^88+424x^89+218x^90+156x^91+48x^92+42x^93+18x^94+10x^95+6x^97+2x^98+4x^99+2x^103 The gray image is a linear code over GF(2) with n=320, k=15 and d=140. This code was found by Heurico 1.13 in 17.2 seconds.