The generator matrix 1 0 1 1 1 X^3+X^2+X 1 1 X^3 1 1 X^2+X 1 1 X 1 X^3+X^2 1 1 X^2 1 1 1 X^3+X 1 1 X^2+X 1 1 X^3+X^2+X X^3 1 1 1 1 X^2 1 1 0 1 1 X^3+X^2 X^3+X 1 1 X 1 1 X^3 1 X^2 X 1 1 1 1 X X^3+X 1 0 1 X^2+X 1 X 1 0 X^3+X^2 X^3+X^2 0 X^2+X X^3+X^2+X X^3+X^2+X X^3+X^2+X X^3+X^2+X X^3+X^2+X X^3+X X 1 1 0 0 X^3 1 1 1 X 1 X 1 1 0 1 X+1 X^3+X^2+X X^2+1 1 X^3+X^2+1 0 1 X^3+X^2+X X+1 1 X^3+X^2 X^2+X+1 1 X 1 1 X^3+X^2+X+1 1 X^3+X^2 X X^3+1 1 X^3 X^3+X+1 1 X^2+X X^3+1 1 1 X+1 X^3+X X^3+X^2 X^3+1 1 X^2+X+1 X^3+X^2+1 1 X X^3 1 1 X^3+X^2 X^3+X^2+1 1 X^2+X+1 X^3+X X X^2 1 1 X^2+1 X^2 X X+1 X^3+X^2 1 X^3+X^2 1 X^3+X+1 1 X^3+X^2+1 1 X^3+X^2+X+1 1 1 1 1 1 1 1 1 1 1 1 0 X^3+X^2+X X^3+X 1 1 1 X^2+X+1 X^3+X^2 X^3 X^3+X X^2 X^3+X X^3+1 0 0 0 X^2 0 0 0 0 X^3+X^2 X^3+X^2 X^2 X^3+X^2 X^2 X^2 X^3+X^2 X^3 X^3+X^2 X^3 X^3 X^2 X^2 X^3 X^3 X^3 X^3+X^2 0 0 X^3 X^3+X^2 X^2 X^3+X^2 0 0 X^3 X^2 X^2 X^2 X^3 X^3+X^2 X^3+X^2 0 X^3+X^2 X^3 X^2 X^3 X^3+X^2 0 X^3 X^2 X^3+X^2 X^3+X^2 0 X^3+X^2 X^3 0 0 X^2 X^3+X^2 X^2 X^3+X^2 X^3 X^3 X^2 X^2 X^3 X^2 0 0 X^3+X^2 X^3+X^2 X^3+X^2 X^3+X^2 0 X^3+X^2 X^3 0 X^3 X^3+X^2 X^3+X^2 X^3+X^2 X^2 X^2 0 X^2 X^3+X^2 X^3 X^3+X^2 X^2 X^2 0 X^3+X^2 0 0 0 X^3+X^2 X^3 X^3+X^2 X^2 X^2 X^3 X^3 X^3+X^2 X^3+X^2 X^2 0 X^3+X^2 X^3 0 X^2 X^3+X^2 X^3 0 X^3+X^2 X^3 X^3+X^2 X^2 X^3+X^2 0 X^3+X^2 X^2 X^3 X^3+X^2 X^3 0 0 X^3 X^2 0 0 X^3+X^2 X^3 X^3 X^2 0 X^3+X^2 X^3+X^2 X^3 X^2 X^2 0 X^3 0 X^3 X^3 0 X^3+X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^2 X^2 X^2 0 X^3 X^3 0 X^2 X^3+X^2 X^3 0 X^3+X^2 X^2 0 0 X^3+X^2 X^3 X^2 X^3+X^2 X^2 X^3+X^2 X^3+X^2 X^2 X^3 X^3 0 X^3 X^3 0 X^3+X^2 0 X^3+X^2 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+164x^85+263x^86+572x^87+531x^88+376x^89+460x^90+482x^91+352x^92+350x^93+248x^94+182x^95+54x^96+30x^97+4x^98+6x^99+1x^100+4x^101+4x^103+2x^105+2x^108+2x^109+2x^111+2x^112+1x^118+1x^124 The gray image is a linear code over GF(2) with n=720, k=12 and d=340. This code was found by Heurico 1.16 in 0.922 seconds.