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 X 1 1 1 1 X 1 1 1 1 0 1 1 1 X^3+X^2 1 0 X 1 1 1 1 X X^3 X^3+X^2 X 0 X^3 1 1 1 X 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^3+X^2 X^2+X X^3+X^2+X X^3+X^2 X^3 X^3+X X^3 X^3+X^2 X^3+X^2+X 0 X^3+X X^3+X X^2 X^3+X X^3+X X^2 X^3+X^2+X X^2 X^2 X^3 X^3+X X^2 X^3+X^2+X X^2+X 0 X X^2 X^2 X^3+X X^2+X X^3+X^2+X 0 X^2 X^2+X 0 X^3+X^2+X X X X^3 X^3+X^2+X X^3 0 0 X^3+X^2 X 0 X^2+X X^3+X X X^3+X^2 X^3 X^3+X^2 X X X X 0 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^2 X^3+X^2 X^3+X^2+X X^2+X 0 X^3+X 0 X^2+X 0 X^3 X^3+X^2 X^2 X X^3+X X^2 X^3+X X^3+X^2+X X^3 X^3+X^2 X X^3+X^2 X X X X^3 X^3+X^2 X^3+X 0 X^2+X X^3 X^2+X X^3 X^3 0 X^2 X^2+X 0 X^2 X^3+X^2+X 0 X^2 X X^3+X^2+X X^3+X^2+X X^2+X X X^2+X 0 X^2+X X^2+X X X^3+X X^3+X^2+X X^3+X^2+X X X^3 X^3+X^2 X^3 0 X^2+X X^3 X^2 X^2+X 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 0 0 X^3 0 0 X^3 X^3 X^3 X^3 X^3 X^3 0 X^3 0 X^3 0 0 X^3 0 X^3 0 0 X^3 X^3 0 0 0 X^3 X^3 0 X^3 X^3 0 X^3 X^3 0 0 X^3 0 0 X^3 0 X^3 0 X^3 X^3 X^3 X^3 0 X^3 0 0 X^3 X^3 0 0 X^3 0 0 0 X^3 X^3 0 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 0 0 0 0 X^3 X^3 X^3 0 X^3 0 0 0 X^3 X^3 X^3 0 0 0 X^3 0 0 X^3 0 X^3 X^3 X^3 X^3 X^3 0 0 0 0 0 X^3 0 X^3 X^3 X^3 0 X^3 0 0 0 0 X^3 X^3 0 X^3 X^3 X^3 X^3 X^3 0 0 X^3 0 X^3 X^3 X^3 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+414x^80+40x^81+540x^82+344x^83+500x^84+544x^85+460x^86+288x^87+538x^88+56x^89+276x^90+8x^91+44x^92+20x^94+6x^96+16x^98+1x^144 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 27.5 seconds.