The generator matrix 1 0 1 1 1 X^3+X^2+X 1 1 X^3 1 1 X^2+X X^2 X^3+X 1 1 1 1 X 1 1 X^3+X^2 1 1 X^3+X X^3 1 1 X^3+X^2+X 1 1 X^3+X 1 1 X^2 1 1 X^2 1 0 X^3+X^2+X 1 1 1 X^3+X^2+X 1 1 0 1 1 0 X X^2+X X X^3 X^3+X X X^2 X^2 X^3+X^2 X^3+X^2 X^3+X^2+X 0 X^2+X X^3+X 1 1 1 1 1 1 1 1 1 1 X^2+X X X^2 X^2 1 1 X^3 1 1 X^2 X X^2 X^2 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 1 1 X^3 X^2+1 X^3+X X^3+X+1 1 0 X+1 1 X^3+X X^2+1 1 1 X^2 X^3+X^2+X+1 1 1 X 1 X^2+X+1 X^2+X 1 X^3+X^2 1 1 X^2 1 1 X^3+1 X^3+X X^2+X+1 1 X^3+X^2+X 1 1 X^2 X^2+X+1 1 1 1 1 1 1 X^2 1 1 1 1 1 1 1 1 X^3+X+1 X^2+X X^3+X^2+X+1 X^2+X 0 0 X^3+1 X+1 X^2+X+1 X^3+X+1 1 X^3 1 1 X^3 X^3+X+1 1 X^3+1 0 X^3+X^2 X^2+X X^3 1 0 0 X^2 0 0 0 0 X^3+X^2 X^2 X^2 X^3+X^2 X^2 X^2 X^3+X^2 X^3 X^2 X^3 X^3 X^3 X^3+X^2 X^3 X^3 X^2 X^3+X^2 X^3+X^2 0 X^3+X^2 X^2 X^3+X^2 X^2 X^3 X^3 X^3 0 X^2 X^3+X^2 0 X^3 X^3 X^3+X^2 X^3+X^2 X^3+X^2 X^2 X^3+X^2 0 X^2 0 X^2 0 X^3 X^2 0 X^3 X^3+X^2 X^3 0 X^2 X^3+X^2 0 X^3 X^2 X^2 0 0 X^2 0 X^3+X^2 X^2 X^3+X^2 X^3 X^3 0 0 X^3+X^2 X^3+X^2 0 0 X^3+X^2 X^2 X^3+X^2 X^3+X^2 X^3 X^3 X^2 X^3+X^2 X^2 X^3 0 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 0 X^2 X^2 X^2 X^3 X^3+X^2 X^3+X^2 0 0 X^3 X^3+X^2 X^3 X^3+X^2 X^2 X^3 X^2 X^3 X^3 X^3+X^2 X^3 X^2 0 X^3+X^2 X^2 X^3 X^2 X^3 X^2 0 X^3+X^2 0 0 0 X^3+X^2 X^3+X^2 X^2 X^2 0 0 0 X^3+X^2 0 X^3 X^3+X^2 0 X^3 X^3 X^3+X^2 X^2 0 X^3+X^2 X^3 X^3+X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^3 X^3+X^2 0 0 0 X^3+X^2 X^3 X^2 X^2 0 X^3 X^3+X^2 X^2 0 0 X^3+X^2 X^3+X^2 X^3 X^3+X^2 0 generates a code of length 88 over Z2[X]/(X^4) who´s minimum homogenous weight is 83. Homogenous weight enumerator: w(x)=1x^0+156x^83+433x^84+356x^85+720x^86+286x^87+417x^88+282x^89+518x^90+274x^91+361x^92+158x^93+87x^94+14x^95+18x^96+2x^97+1x^98+4x^99+2x^107+2x^108+2x^109+1x^118+1x^122 The gray image is a linear code over GF(2) with n=704, k=12 and d=332. This code was found by Heurico 1.16 in 0.984 seconds.