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 X 1 0 1 1 1 0 X^2 1 1 X 1 1 1 X^2 X^2 0 1 0 1 1 1 X X 1 1 0 1 0 1 X 1 0 X^2 1 X 1 X 1 X 0 X 0 0 0 0 0 0 X^2 X X^2+X X^2+X X X X^2+X X^2+X X^2 X^2 0 X X X^2+X X 0 X X 0 X^2+X X X^2 X^2 X^2 X^2+X X^2+X X^2+X X^2+X X X^2+X X^2+X X^2+X X X 0 X^2+X X^2 0 X X X X 0 X 0 X 0 0 0 X^2 X^2 X X^2 X^2 X X^2 X^2+X X X^2 X^2 0 X^2 0 X X^2+X 0 0 0 X 0 0 0 X X^2+X X^2+X X X X^2 X X X^2 0 X^2 X^2+X X^2+X X^2+X 0 X X^2+X X^2+X 0 X^2+X X^2+X X^2 X^2 0 0 X^2 X^2 X^2+X X X^2+X X 0 X^2 X X X 0 0 X^2+X X^2+X X^2 X^2+X 0 X^2 0 X^2 0 X X^2 X^2 0 X^2+X X X^2+X X 0 0 X X^2+X 0 X X X^2 X^2 0 X^2+X X^2+X 0 0 0 0 X 0 X X X 0 X^2 0 X X^2+X X^2+X X X^2 X^2 0 0 0 X^2 X^2 X^2+X X X^2+X X X 0 X X^2 X^2+X X^2+X X^2+X X X^2+X X^2+X X X 0 X^2 X^2 X^2+X X 0 X^2+X X^2+X X 0 X X^2+X X^2 X X X^2 0 X^2+X 0 X^2 X^2+X X X^2+X 0 X 0 X^2 0 X^2 X^2 X X^2 X^2 X^2 X X 0 0 0 0 X X X^2 X^2+X X X^2 X 0 X 0 X X X^2+X X^2+X 0 X^2 X X X^2 0 X^2 X^2+X X^2+X 0 X 0 X^2 X X^2+X X 0 X^2+X 0 X 0 X^2+X X^2+X X 0 X^2 0 X^2+X X X^2+X X^2 X X X^2 X^2+X 0 X^2 0 X^2+X X^2 X 0 0 X X X X^2+X X^2+X X^2+X X 0 X^2+X X X^2 X^2 X 0 0 0 0 0 X^2 X^2 X^2 0 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 X^2 0 0 0 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0 0 0 X^2 0 0 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 0 0 0 X^2 0 X^2 0 0 generates a code of length 74 over Z2[X]/(X^3) who´s minimum homogenous weight is 65. Homogenous weight enumerator: w(x)=1x^0+52x^65+109x^66+138x^67+208x^68+228x^69+235x^70+284x^71+289x^72+374x^73+413x^74+346x^75+301x^76+284x^77+214x^78+138x^79+124x^80+72x^81+82x^82+64x^83+33x^84+40x^85+30x^86+18x^87+2x^88+6x^89+4x^90+4x^91+2x^92+1x^110 The gray image is a linear code over GF(2) with n=296, k=12 and d=130. This code was found by Heurico 1.16 in 1.6 seconds.