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 1 1 1 1 1 1 1 1 1 1 1 1 1 X X 1 1 1 1 1 1 1 1 1 1 1 1 1 X^2 1 X^2 X^2 X 1 0 X^3+X^2 0 X^3+X^2 0 X^3+X^2 0 X^3+X^2 0 X^3+X^2 0 X^3+X^2 0 X^3+X^2 0 X^3+X^2 0 X^3+X^2 0 X^3+X^2 0 X^3+X^2 0 X^3+X^2 X^3 X^2 X^3 X^2 X^3 X^2 X^3 X^2 0 X^3+X^2 X^3 X^2 X^3 X^2 X^3 X^2 0 X^3+X^2 X^3 X^2 X^2 X^3 X^3 X^2 0 X^2 X^3 X^2 X^3 X^3+X^2 X^3 X^2 0 X^3+X^2 X^3 X^2 X^3 X^2 X^3 X^2 X^3+X^2 X^3+X^2 0 X^3+X^2 0 X^3+X^2 0 X^3+X^2 0 0 X^3 X^3+X^2 0 X^2 X^3 X^3+X^2 X^3+X^2 X^3+X^2 X^3 0 0 0 0 X^3 0 0 0 X^3 0 0 0 0 0 X^3 0 X^3 0 0 X^3 0 X^3 0 X^3 0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 0 0 0 0 X^3 X^3 X^3 X^3 0 0 0 0 X^3 X^3 0 0 X^3 X^3 0 0 X^3 X^3 X^3 X^3 0 0 0 0 0 0 0 0 0 0 X^3 X^3 X^3 X^3 X^3 0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 0 0 0 0 0 X^3 0 0 0 X^3 0 0 0 0 0 X^3 0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 0 X^3 0 X^3 0 X^3 0 X^3 0 0 X^3 X^3 X^3 0 0 X^3 0 0 X^3 X^3 X^3 0 0 X^3 X^3 0 0 0 0 X^3 X^3 X^3 0 0 X^3 X^3 X^3 0 0 0 0 0 0 X^3 X^3 X^3 0 X^3 X^3 0 0 0 0 X^3 0 X^3 X^3 0 0 0 0 0 0 0 X^3 0 X^3 0 0 X^3 X^3 X^3 X^3 X^3 0 X^3 X^3 0 X^3 0 0 X^3 0 X^3 X^3 0 X^3 0 0 X^3 0 X^3 0 X^3 0 X^3 0 X^3 0 X^3 0 X^3 0 0 0 X^3 X^3 0 X^3 0 X^3 X^3 X^3 0 X^3 0 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 X^3 X^3 0 X^3 X^3 X^3 0 0 0 0 0 0 0 X^3 0 X^3 X^3 X^3 X^3 0 X^3 0 X^3 X^3 0 0 X^3 X^3 X^3 X^3 0 0 0 0 X^3 X^3 X^3 X^3 0 0 0 0 0 0 0 0 0 0 X^3 X^3 X^3 X^3 0 0 X^3 X^3 X^3 0 0 X^3 X^3 X^3 X^3 X^3 0 0 0 X^3 X^3 X^3 X^3 0 0 X^3 0 X^3 0 0 0 0 X^3 X^3 X^3 0 0 X^3 0 X^3 0 X^3 0 X^3 0 generates a code of length 85 over Z2[X]/(X^4) who´s minimum homogenous weight is 80. Homogenous weight enumerator: w(x)=1x^0+17x^80+18x^81+61x^82+94x^83+118x^84+420x^85+114x^86+92x^87+50x^88+10x^89+14x^90+6x^91+6x^92+1x^94+1x^98+1x^158 The gray image is a linear code over GF(2) with n=680, k=10 and d=320. This code was found by Heurico 1.16 in 0.703 seconds.