The generator matrix 1 0 0 1 1 1 0 X^3 1 1 X^3 X^2 1 1 1 1 1 1 X^2+X X X 1 X^3+X 1 X^3+X X^3+X 1 1 X^3+X^2 1 1 0 1 0 X^2 1 1 1 X^3+X^2 1 X^2+X 1 X^2+X 1 X^3+X^2+X X^3+X^2+X 1 1 X 1 1 1 X^3+X 1 1 X^3 X^3+X 1 1 1 1 X^3+X 1 X^2 1 X^3+X^2 1 X 1 X^2 1 1 X^3+X 1 1 1 X 1 0 1 1 X^3+X^2 1 1 X^3+X^2 X^3+X^2+X 1 X^3+X^2 1 1 0 1 0 0 X^2+1 X^2+1 1 X^3+X^2+X X^3 X^3+X^2+1 1 1 X^3+X^2 1 X^2+X X^3+X+1 X+1 X^3+X^2+X X^3+X 1 1 X^2+X+1 1 X^2+X X^3 1 X+1 X^2+X X^2 X^3+X+1 X^3+X 1 0 1 1 X^2+X+1 X^2 X^3+X+1 1 X X^2+X X^3+1 1 X^2+1 1 X^3+X^2 1 X^2+X 1 X^2 X^2+X X^3+X^2 1 X+1 1 X^3+X 1 X^3+X X^3+X^2+X+1 X 0 1 X^2+X+1 X^3 X^3+X^2 1 0 X X^2 1 X X^3+X 1 X^3+1 X^3+X^2+X+1 X^2+1 0 X^3+X 1 X^3 X^2+1 0 X^2 X^3+X 1 1 X^3+X^2 1 X^3+X^2+X 0 0 0 1 X+1 X^3+X+1 X^3 X^3+X^2+X+1 1 X^3+X^2+X X^2+1 1 X^3+X X^3+X^2+1 X X^3+X+1 X^3 X^3+X^2+1 X^3+X^2+X 1 X+1 X^2 X^3+X X^2+1 X^2 1 X X^3+X+1 1 1 X^3+X^2 0 X^2+X X^3+1 1 0 X^3+X^2+X+1 X^2+X X X^3+X+1 X^3+X^2+X 1 X^3+X^2 X^2 X+1 1 1 1 X^3+X^2+X+1 X^2+X X^3 X^3+X^2+1 X^2+X+1 X^3+X^2+1 X^3+1 X^3+X 1 X^3+X+1 X^3+X^2+X X^3+X X^2+1 X X^2+X X^2+X 1 X^2+X+1 X^3+1 X^2 1 X^3+1 X^2+X+1 X^3+X+1 X^2 1 X^3+X^2+1 X^3+X^2 X^2 1 X+1 X^3+X^2 X^2 X^2+X+1 1 X^3+X+1 X^3+X^2 X^3+X^2+X X+1 X X^3+X X^3+1 0 0 0 0 X^3 X^3 0 X^3 X^3 X^3 0 0 X^3 0 X^3 0 X^3 X^3 0 0 0 X^3 0 X^3 X^3 X^3 0 X^3 0 X^3 0 0 0 X^3 X^3 X^3 0 X^3 X^3 0 0 0 X^3 0 0 0 X^3 X^3 X^3 0 X^3 0 X^3 0 0 0 0 X^3 X^3 X^3 X^3 0 X^3 0 0 0 X^3 X^3 X^3 0 0 0 0 X^3 X^3 X^3 0 0 X^3 X^3 0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 0 X^3 X^3 generates a code of length 90 over Z2[X]/(X^4) who´s minimum homogenous weight is 85. Homogenous weight enumerator: w(x)=1x^0+194x^85+767x^86+1110x^87+1095x^88+826x^89+1032x^90+748x^91+736x^92+530x^93+404x^94+250x^95+205x^96+74x^97+58x^98+84x^99+50x^100+24x^101+1x^102+2x^106+1x^112 The gray image is a linear code over GF(2) with n=720, k=13 and d=340. This code was found by Heurico 1.16 in 3.39 seconds.