The generator matrix 1 0 1 1 1 X^2+X 1 X^3+X^2 1 1 1 X^3+X 1 1 X^3 1 X^3+X^2+X 1 1 X^2 1 X 1 1 1 1 1 X^3+X^2 1 1 X^2+X 1 1 X^3+X^2+X 1 1 X 1 X^3 1 1 1 1 X^2 1 0 1 X^3+X^2+X X 1 X 1 1 1 1 1 1 X^3 1 1 1 1 1 1 1 1 X^3 1 1 1 1 1 1 X^3+X^2 X 1 1 1 1 0 X X^3 X^3+X^2 0 1 0 1 X+1 X^3+X^2+X X^3+X^2+1 1 X 1 X^2+X+1 X^3 1 1 X^2 X+1 1 X^2+1 1 X^3+X^2 X^3+X^2+X+1 1 X^3+1 1 0 X^3+X^2 X^2+X X^3+X X+1 1 X^3+X X^2+1 1 X^2+X X^3+X+1 1 X^3+X^2+1 X^3+X^2+X 1 X^2 1 X^3+X^2+X 1 X^3 X^3+X^2+X+1 1 X^3+X 1 X+1 1 X^3+X^2 X^3+1 1 X^2 X^3+1 X^2+X+1 X^2+X X^2 X^3+X^2 1 X X^3+X^2 X^3+X 0 X^3+X X^2+X X^2 X^3+X 1 X^2 X^3+X 0 X^3+X^2+X X^2+X X^3+X^2 1 1 X^3 X^2+X X^3+X^2+1 X^3+X^2+X 0 X^3+X^2+X X 1 1 X^3+X^2 0 0 X^2 X^2 X^3+X^2 0 X^3+X^2 0 X^2 X^2 X^3+X^2 0 X^3+X^2 X^3 X^2 X^3 X^2 0 X^3 X^2 X^3 X^2 0 0 0 X^3 X^3 0 0 X^3 0 0 X^2 X^2 X^2 X^2 X^3+X^2 X^3+X^2 X^2 X^3 X^3+X^2 X^2 0 X^3+X^2 X^3+X^2 X^3 X^3+X^2 X^3 X^3 0 0 0 X^3 X^3+X^2 X^3+X^2 X^2 X^3 X^3+X^2 X^2 X^3+X^2 0 X^3+X^2 X^3 X^2 X^3 X^2 0 0 0 X^2 X^3 0 X^3 X^3+X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^3 X^3+X^2 X^2 X^2 X^2 X^3 X^2 X^3+X^2 0 0 0 X^3 0 X^3 X^3 X^3 X^3 0 X^3 0 0 X^3 0 X^3 0 0 0 X^3 0 X^3 X^3 X^3 0 X^3 0 0 X^3 0 0 0 0 X^3 X^3 0 0 X^3 X^3 X^3 0 X^3 X^3 0 0 X^3 X^3 X^3 0 X^3 X^3 X^3 X^3 X^3 0 0 0 0 X^3 0 0 X^3 0 X^3 X^3 0 0 0 0 X^3 X^3 X^3 0 0 X^3 0 X^3 0 X^3 X^3 0 X^3 0 0 0 0 0 0 0 X^3 0 X^3 X^3 X^3 X^3 0 X^3 0 0 0 X^3 X^3 X^3 0 0 X^3 X^3 X^3 0 0 0 X^3 X^3 0 0 0 X^3 X^3 0 X^3 X^3 0 0 X^3 X^3 0 X^3 X^3 X^3 0 0 0 X^3 X^3 0 0 X^3 X^3 0 0 X^3 0 X^3 0 X^3 X^3 0 0 X^3 X^3 0 X^3 0 0 0 0 X^3 X^3 0 0 0 0 X^3 X^3 X^3 X^3 0 X^3 0 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+118x^80+292x^81+490x^82+640x^83+448x^84+476x^85+328x^86+408x^87+375x^88+276x^89+86x^90+72x^91+52x^92+12x^93+2x^94+8x^96+2x^100+6x^102+2x^104+1x^116+1x^124 The gray image is a linear code over GF(2) with n=680, k=12 and d=320. This code was found by Heurico 1.16 in 0.953 seconds.