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 X 1 1 X 1 1 1 1 1 1 1 1 1 X 0 1 X^2 1 1 X 1 1 1 X X 1 1 0 1 1 X^2 1 1 X^2 1 1 X^2 1 X^2 0 1 X 1 1 1 X 1 0 X 0 0 0 0 0 0 X^2 X X^2+X X^2+X X^2+X X^2+X X^2+X X^2+X X^2 X^2+X X^2 X^2+X X X^2 X^2 X^2+X X 0 X^2 0 X X X^2+X 0 X^2 X^2+X X X X^2+X X 0 X 0 0 0 X^2+X X^2+X X^2 0 X^2+X 0 X X^2+X X^2 X^2+X X X^2 X^2+X 0 X^2+X X^2 0 X^2 X^2 X X^2 0 X X^2 0 X^2 X^2 X X X^2+X X^2 0 X^2+X 0 X^2 X^2+X X X 0 0 0 X 0 0 0 X X^2+X X^2+X X X X^2 X^2+X X 0 X^2 0 X^2 X 0 X 0 X^2 X^2 X^2+X X X^2 X 0 X X^2+X X 0 X^2+X X^2+X X^2+X 0 X^2 X X^2 X^2+X 0 X X 0 0 X^2+X X^2+X X^2+X X^2+X X^2+X X 0 X^2 0 X^2+X X 0 X X^2+X 0 X X X^2+X X^2+X X^2 X^2 X^2 X X 0 X^2 X X^2 0 X^2+X 0 X^2+X X X^2+X X^2+X X 0 0 0 X 0 X X X 0 X^2 0 X X^2+X X X X^2+X X^2 X^2 0 X^2 X^2+X X 0 X 0 X X^2+X X^2 X^2 X^2+X 0 X^2+X X^2 0 X^2 X^2 X^2 0 X^2+X X^2+X X^2+X X^2+X 0 X^2+X X 0 X^2+X X^2+X X^2 0 0 X 0 X^2+X 0 X^2 X X^2 0 X^2+X X^2+X X^2 X X^2 0 X X^2 X X^2 X^2+X X^2+X X^2 X 0 0 0 X X X^2 X^2+X 0 X^2+X 0 0 0 0 X X X^2 X^2+X X X^2 X 0 X X^2 X^2+X X^2 0 X X^2+X X^2 X^2+X 0 X X^2+X 0 0 X^2+X 0 X X^2 X^2+X X^2+X X^2 X^2 X 0 X^2 X^2+X X^2 0 X X X^2 X^2+X X^2+X X^2+X 0 0 X^2 X^2+X X^2+X X 0 X^2+X X 0 X^2+X 0 0 X^2+X 0 X^2+X X^2 0 0 X X^2 0 X X X^2 X^2+X X^2+X X X X X^2+X X X X^2 X^2 X 0 0 0 0 0 X^2 X^2 X^2 0 0 0 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 0 X^2 0 X^2 0 0 X^2 0 0 0 0 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 X^2 X^2 0 0 X^2 0 X^2 0 0 0 X^2 X^2 0 0 0 0 0 X^2 0 0 0 0 0 X^2 X^2 generates a code of length 82 over Z2[X]/(X^3) who´s minimum homogenous weight is 73. Homogenous weight enumerator: w(x)=1x^0+66x^73+105x^74+118x^75+219x^76+142x^77+354x^78+140x^79+577x^80+114x^81+668x^82+86x^83+535x^84+78x^85+317x^86+84x^87+135x^88+62x^89+66x^90+62x^91+54x^92+34x^93+21x^94+16x^95+11x^96+14x^97+5x^98+6x^99+3x^100+2x^101+1x^132 The gray image is a linear code over GF(2) with n=328, k=12 and d=146. This code was found by Heurico 1.16 in 2.24 seconds.