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 1 1 1 1 1 1 1 1 1 1 1 1 X 1 1 1 1 1 X 1 1 0 1 1 1 X^2 1 1 X 1 1 1 1 1 1 1 0 X^2 X^3 X^2 X 0 X 0 X^3+X^2+X X^2 X^2+X X^3+X^2 X 0 X^2+X X^3 X^2+X X^3+X X^2 X^2 X 0 X^2+X X^2 X^3+X X^3 X^3+X X^3 X^3+X X^2+X 0 X^3+X X^2 X X^3 X^2+X 0 X^2 X 0 X^3+X^2+X X^3+X^2 X^3+X^2+X X^3+X 0 0 X^2+X X^3+X X^3 X^2 X^3+X X^3+X^2 X^3+X 0 X X^3+X^2 X^3+X^2+X 0 X^3+X X^2+X X^2 X^3+X X^2+X X^3+X^2 X^3+X^2 X X^3+X^2+X X X^3+X^2+X X^3 0 X^3 X^2 X X^2+X X^2+X X^2 X^3+X^2+X X^2+X X^3+X^2 X^3 X X^2 X X^3+X^2+X 0 0 X^3+X^2 0 X^2 0 X^3 0 X^2 X^2 X^3 X^3+X^2 X^3+X^2 X^3+X^2 0 X^2 0 X^3+X^2 X^3 X^3+X^2 X^2 X^3 X^2 0 0 0 X^3+X^2 X^3+X^2 0 X^2 X^2 X^3 X^3 X^3 X^3+X^2 X^3+X^2 X^3 X^3 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 X^3+X^2 X^3 X^2 0 X^3 X^3 0 X^3 X^2 X^2 X^2 0 X^3+X^2 0 X^3 X^3 X^3+X^2 X^3 X^3 X^2 0 X^3 X^2 0 X^2 X^3+X^2 X^3+X^2 X^2 X^2 X^3+X^2 0 X^3+X^2 0 0 0 X^3+X^2 0 X^3 X^3 X^2 X^2 X^2 X^2 0 0 X^2 X^3+X^2 X^2 X^3 X^3+X^2 X^3+X^2 X^3 0 X^3+X^2 X^3+X^2 X^3 0 X^3+X^2 X^2 X^3+X^2 X^3+X^2 0 X^3 X^3 X^3 X^3+X^2 X^3+X^2 X^2 X^3+X^2 X^2 X^3 0 X^3 X^3+X^2 X^3 X^3+X^2 X^3 X^3 X^2 X^2 X^2 X^3 X^3 X^2 X^2 X^3 X^2 0 X^2 X^2 X^3+X^2 X^3+X^2 X^2 X^3+X^2 0 0 X^3+X^2 X^3 0 X^2 X^3+X^2 X^3 X^3 0 0 X^2 X^3 0 0 X^3 X^2 0 0 0 0 0 X^3 X^3 X^3 X^3 0 0 0 X^3 0 X^3 X^3 X^3 0 0 X^3 0 0 X^3 0 0 X^3 0 X^3 X^3 0 X^3 X^3 X^3 0 0 0 0 0 X^3 X^3 X^3 0 X^3 X^3 X^3 X^3 0 X^3 0 X^3 X^3 0 X^3 X^3 0 X^3 0 0 0 0 0 X^3 X^3 0 0 X^3 0 X^3 0 X^3 0 0 X^3 X^3 X^3 X^3 0 X^3 0 0 0 generates a code of length 80 over Z2[X]/(X^4) who´s minimum homogenous weight is 74. Homogenous weight enumerator: w(x)=1x^0+228x^74+350x^76+96x^77+596x^78+416x^79+827x^80+416x^81+564x^82+96x^83+256x^84+124x^86+92x^88+24x^90+9x^92+1x^140 The gray image is a linear code over GF(2) with n=640, k=12 and d=296. This code was found by Heurico 1.16 in 130 seconds.