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 0 1 1 1 1 1 1 X^3 1 X X 1 1 X^2 X 1 1 1 X^2 1 X 1 0 1 X^2 X^3+X^2 1 0 X X^3+X^2 1 X 1 0 X 0 X X^3 0 X^2+X X^3+X^2+X 0 X^3 X^3+X X X^3 X^3+X^2+X X^3 X^3+X^2+X X^2 X^3+X X^3+X^2 X^3+X X^2 X^3+X^2+X X^2 X^2+X X^3+X^2+X X^2 X^2+X X^2 X 0 X X^3 X^3+X^2 X^3+X^2+X X^3+X^2+X X^2 0 X X^3+X X^3 X^3+X^2 X X^3+X^2 X^3+X^2 X^3+X^2+X X^2+X X^2 X^2+X X^2 X^3+X X^3 X^3+X^2+X X^2 X^2 0 X X^2 X^3 X^2 X^3 X^3+X X X^2+X X^3+X^2+X X^3+X X^2 X^3+X^2+X 0 X^3 X^3+X^2 X^3+X^2 X^3 X^2 X^3+X X^3+X X^3 X X^3+X^2 X^3+X X^2 X X^3 X X X X X^3+X^2+X X^2 X X^3+X^2 0 0 0 X X 0 X^3+X^2+X X^2+X X^3 X^2 X^3+X^2+X X^3+X^2+X X^2 X^3+X X^2 X^3+X^2 X X^2 X^2+X X^3+X X^3+X^2 X^2+X X^2+X X^2 0 0 X^2 X^3+X^2+X X^3+X^2+X 0 X X^2+X X^3 X^2+X X X^3+X^2 X^3+X^2 0 0 X X X^3 X^2+X X X^3+X X^3+X^2 X^2+X 0 X^3+X^2 X^3+X^2+X X^3 X^2+X X^3 0 X^3+X X^2+X X^2 0 X^2 X X^2 X^2 X X^3+X X^3+X X X X^3 X X^3+X^2+X X^3+X^2 X^2 X X X^2 X^3+X^2 X^3+X^2 X^3+X^2+X X^3 X^2+X X^3+X^2 X^3+X^2 X^2 X^2 X^3+X^2 X^3+X^2 X^3 X X X^3 X^2+X X^3 0 0 0 X^2 X^2 X^3+X^2 0 X^3+X^2 X^2 X^3 X^3+X^2 0 X^2 X^3+X^2 0 X^3 0 X^3 X^3+X^2 X^2 0 X^2 X^2 0 X^2 X^3+X^2 X^3+X^2 X^3 X^3 X^3+X^2 0 X^3 X^3+X^2 0 0 X^3 X^3+X^2 X^2 X^3+X^2 X^3 0 X^2 X^2 X^3 X^3 X^3 X^3+X^2 X^2 X^2 X^3+X^2 0 X^3 X^3 0 X^2 X^3 X^2 X^3 X^3+X^2 X^3+X^2 X^3+X^2 0 X^2 X^3+X^2 X^3 X^3 0 X^3+X^2 0 0 0 X^3+X^2 0 0 0 X^3 X^3+X^2 X^3+X^2 0 X^3+X^2 X^2 X^2 X^3 X^3 X^3+X^2 X^3+X^2 X^2 0 X^2 X^3 0 generates a code of length 91 over Z2[X]/(X^4) who´s minimum homogenous weight is 85. Homogenous weight enumerator: w(x)=1x^0+74x^85+229x^86+274x^87+370x^88+468x^89+401x^90+624x^91+392x^92+416x^93+287x^94+210x^95+174x^96+68x^97+33x^98+24x^99+18x^100+10x^101+9x^102+4x^103+4x^104+4x^105+1x^110+1x^152 The gray image is a linear code over GF(2) with n=728, k=12 and d=340. This code was found by Heurico 1.16 in 1.28 seconds.