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 0 X X 1 1 1 1 1 1 1 X^2 1 X^2+X 1 1 X 1 1 X^2+X 1 1 1 1 X X 1 1 0 1 1 1 X^2 1 1 1 0 1 1 1 X^2+X 1 X^2+X X X^2+X X X 1 1 X^2+X 0 1 1 1 1 X^2 1 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 0 1 X+1 X^2+X X^2 X^2+1 1 X^2+X X 1 1 1 X^2+1 1 X^2+X X^2+X X+1 1 X^2 X X^2+X+1 X^2+X 1 0 X^2+X+1 X^2 X 1 X^2+1 1 X^2+X X X^2+X+1 0 1 0 0 X^2+X+1 1 1 1 X^2 1 X^2 X 0 X^2+X 1 1 X^2+1 X^2+X+1 0 X^2 0 0 X^2 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+X+1 X^2+X X+1 X^2+X X+1 X^2 X^2+1 X X^2 X X+1 1 X+1 X X+1 X 1 0 X^2+1 X^2+1 X^2 0 1 0 1 X^2+X+1 0 X X^2 0 X^2+1 X^2 X+1 X+1 X+1 0 X X^2+X+1 X^2+X 1 X^2+X+1 X^2 1 X^2+X 1 1 X^2 X^2+X+1 X^2+X X X^2 X+1 1 X+1 X^2 X^2+1 X^2 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 0 1 X+1 X X^2+1 X^2+1 X X^2+X X+1 X X^2+1 X X^2+1 X+1 1 1 X^2 X^2+X 0 X^2+X X^2+X X^2+X+1 X^2+1 X^2 X^2+1 1 X^2+X+1 X^2+X 0 1 X^2 1 1 X+1 X^2+X+1 X^2+X+1 X^2 0 X^2+1 X^2+X+1 X X^2 X X X^2 X^2 X^2+X X^2 X^2+1 1 0 0 0 X 0 X^2+1 0 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 X+1 X+1 X X+1 X^2+X+1 X^2+1 X+1 X 1 X^2+X X X^2+X+1 0 0 X+1 X 0 X^2+X+1 X^2+1 X X X^2 X 1 1 X+1 1 X X X X^2 X^2 X^2+X+1 1 X+1 X^2+X X^2+1 X^2+1 0 X^2+X X^2 X X+1 X+1 X^2+1 X^2+1 X^2+X+1 X^2+X 0 X+1 X X 0 1 X^2+1 X^2+X generates a code of length 81 over Z2[X]/(X^3) who´s minimum homogenous weight is 71. Homogenous weight enumerator: w(x)=1x^0+100x^71+448x^72+892x^73+1139x^74+1426x^75+1692x^76+2124x^77+2183x^78+2558x^79+2387x^80+2742x^81+2663x^82+2730x^83+2303x^84+2058x^85+1578x^86+1250x^87+896x^88+646x^89+398x^90+284x^91+135x^92+60x^93+35x^94+20x^95+10x^96+4x^97+2x^98+2x^101+2x^102 The gray image is a linear code over GF(2) with n=324, k=15 and d=142. This code was found by Heurico 1.16 in 51.1 seconds.