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 X^3 1 1 X 1 1 1 1 1 1 1 1 1 1 X 1 1 1 1 X^3 1 X^3 X^3+X^2 X 1 1 X^3 1 X^2 1 1 1 1 1 0 0 X 0 X 0 X^3 X^3+X X X^2 X^2+X X^2 X^3+X^2+X X^2 X^3+X^2 X^3+X^2+X X^3+X^2+X 0 X^3+X^2 X X^3+X^2+X X 0 X^3 X^3+X X^2+X X^2 X^2 X^2+X X^3+X 0 X^3+X^2+X X^3+X^2 X X^2 X^3+X^2+X X^3 X^2 X^2 X^3+X X^3+X X^3 X^3+X 0 0 X^3+X X X^3+X^2+X X^3+X X^3+X^2+X X^3+X^2+X X^2+X X^3+X X^3+X^2 0 X^3+X^2 0 X^3 X^3+X^2+X X^3+X X^3+X^2+X X^3+X^2 X^2 X^3+X^2+X X^2 X X^3 X X X^2+X X^3+X^2+X X^3 X X^3+X X X^2+X X^2+X X^2+X X^2 X^3+X^2+X X 0 0 X X X^3+X^2 X^3+X^2+X X^2+X X^2 X^2 X^3+X^2+X X 0 X^3 X^3+X^2+X X^3+X X^2 0 X^3+X X X^2 X^3+X^2+X X X^3+X^2 X^3+X^2 X^3+X^2+X 0 X^2+X X^3 X^3 X^2+X X^3+X X^3+X^2 X^2+X X X^3+X^2 X^3+X^2 0 X^3+X^2+X X X^3+X^2 X X^3 0 X^3+X^2+X X^3+X X^3+X^2 X^3+X^2 X^2+X X 0 0 X^2 X^2 0 X^3+X^2+X X^2 X^3+X^2+X X^2+X X^3 X X X^3+X^2 X^3+X^2+X X^3 X^3+X X^3+X X^2 X^3+X^2 X^3 X X^2 X^3+X X^3+X X^2 X^2+X X^3+X^2+X X^3+X X^3 X^3+X 0 0 0 0 X^3 0 0 X^3 0 X^3 0 X^3 X^3 X^3 X^3 0 X^3 0 X^3 0 X^3 0 0 X^3 0 X^3 0 0 0 X^3 X^3 X^3 X^3 X^3 0 0 0 0 0 0 X^3 X^3 X^3 X^3 0 X^3 X^3 0 0 0 X^3 0 X^3 0 X^3 X^3 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 X^3 0 0 X^3 X^3 0 0 X^3 X^3 0 0 0 0 X^3 X^3 X^3 X^3 X^3 X^3 0 0 0 X^3 0 X^3 X^3 X^3 0 0 X^3 X^3 X^3 0 0 0 0 X^3 X^3 0 X^3 0 0 0 0 0 X^3 X^3 X^3 X^3 X^3 0 0 0 X^3 X^3 X^3 0 0 X^3 0 0 X^3 X^3 0 0 X^3 X^3 X^3 X^3 X^3 0 0 X^3 0 0 0 0 0 0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 0 0 0 generates a code of length 80 over Z2[X]/(X^4) who´s minimum homogenous weight is 75. Homogenous weight enumerator: w(x)=1x^0+332x^75+184x^76+412x^77+224x^78+564x^79+733x^80+576x^81+224x^82+348x^83+158x^84+272x^85+28x^87+2x^88+16x^89+8x^91+9x^92+4x^93+1x^140 The gray image is a linear code over GF(2) with n=640, k=12 and d=300. This code was found by Heurico 1.16 in 125 seconds.