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 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 0 1 1 X X 1 0 X X^3+X^2 X^2+X 0 X^2+X X^3+X^2 X^3+X 0 X^2+X X^3+X X^3+X^2 X^3 X^3+X^2+X X^2 X^3+X 0 X^2+X X^3+X X^3+X^2 X^2+X 0 X^3+X X^3+X^2 X^2+X 0 X^3+X X^3+X^2 X^3+X^2+X X^3 X^2 X 0 X^2+X X^3+X^2 X^3+X X^3+X^2+X 0 X^2 X X^2+X X^3 X^3+X X^2 X^3+X^2+X X^3 X^3+X^2 X 0 X^3 X^2+X X^3+X^2+X 0 X^2+X X^3 X^3+X^2+X X^3+X^2 X^3+X^2 X^2 X^2 X^3+X X^3+X X X 0 X^2+X 0 X^3 X^3 X^2+X X^3+X^2+X X^3+X^2+X 0 X^3 0 X^3+X^2 X^2 X^3+X^2 X^2+X X X^2 X^3 X^2+X X^2+X 0 0 0 X^3 0 0 0 X^3 0 0 0 0 X^3 0 0 X^3 0 0 X^3 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 0 0 0 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 0 X^3 X^3 X^3 X^3 0 0 0 0 0 0 X^3 X^3 0 0 0 0 0 0 0 0 0 X^3 X^3 X^3 X^3 X^3 0 0 X^3 0 0 0 X^3 X^3 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 0 X^3 0 X^3 0 X^3 X^3 0 X^3 0 0 X^3 X^3 0 X^3 X^3 0 0 X^3 X^3 X^3 X^3 0 X^3 X^3 0 X^3 0 X^3 0 0 X^3 0 X^3 X^3 0 0 0 0 0 0 X^3 X^3 X^3 0 X^3 X^3 X^3 X^3 X^3 0 0 0 X^3 X^3 0 X^3 X^3 X^3 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 0 X^3 X^3 0 X^3 0 X^3 0 X^3 0 0 X^3 X^3 0 X^3 0 0 X^3 X^3 0 X^3 X^3 X^3 X^3 0 0 0 0 X^3 0 0 X^3 X^3 0 X^3 X^3 0 0 0 0 X^3 X^3 0 X^3 0 X^3 X^3 X^3 0 0 X^3 0 0 X^3 X^3 X^3 X^3 0 X^3 X^3 X^3 0 0 X^3 0 X^3 X^3 0 0 0 0 0 X^3 0 X^3 X^3 X^3 0 X^3 X^3 0 X^3 X^3 0 0 X^3 X^3 0 X^3 X^3 0 0 0 X^3 X^3 0 X^3 0 X^3 X^3 0 0 0 X^3 0 X^3 0 0 X^3 0 0 X^3 0 X^3 0 X^3 0 X^3 X^3 0 X^3 X^3 X^3 X^3 X^3 0 0 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 0 0 0 0 X^3 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+33x^80+168x^81+103x^82+32x^83+376x^84+624x^85+376x^86+32x^87+102x^88+168x^89+30x^90+2x^98+1x^162 The gray image is a linear code over GF(2) with n=680, k=11 and d=320. This code was found by Heurico 1.16 in 0.781 seconds.