The generator matrix 1 0 0 0 1 1 1 X 1 X^2+X 1 X^3+X 1 1 X^3+X^2 X^3+X^2+X X^2+X X^3 1 1 1 1 X^2 X^3 1 X^3+X 1 X^3 X^3+X^2 0 1 1 0 X 1 X^3+X^2 1 1 X^2 1 1 1 X 1 X^3+X^2 1 1 1 1 X^3 1 X^3+X^2+X 1 X^2 1 X^3+X X^2+X 0 X^3+X 1 1 1 X^3+X^2+X X^3 1 1 1 0 1 1 1 1 1 X^3+X X^2+X X^2+X X^3+X^2 X^2+X 0 1 0 1 0 1 0 1 0 0 X^3 X^3+X^2+1 X^3+X+1 1 X^2 X^2 X^2 1 X^2+X+1 X^2+1 1 X^2+X 1 X^3+X^2+X 1 X^3+X^2+X+1 X^3+X X^2+1 X^2+X 1 X^3+X^2+X 1 X^3 X^3 0 1 X^2+X X^3+1 1 1 X^3+1 X X^3+X^2+1 X^3+X 1 X^3+X^2+X X^3+X^2 X+1 1 X^3+X 1 X^2 X^3+X^2+X+1 1 X^2+1 1 X+1 0 X^2 0 X^3+X^2+1 X X^3+X^2 1 X^3+X X^3+X^2+X+1 X^3+X 1 1 1 X^3+X^2+X 0 X^3 X^3+X^2+X 1 X^3 X^3+X^2 1 X^3+X+1 X^3 X^3+X X^3 X^2+X 1 1 X^3+1 1 1 1 X^3+X^2 0 0 1 0 X^3+X^2 X^3 X^2 X^2 1 1 X^3+X+1 X^3+X+1 X^3+1 X+1 X^2+X+1 1 X^2+X+1 1 X+1 0 X^3+X^2+1 X^2+X+1 X^3+X^2+X X^3+X^2+X X^3 X X X^3+X 1 1 X^3+X^2+X+1 X^3 X^3+1 X X^2+X 1 X^3+X^2+1 X^3+X^2 X^3+X X+1 X X^3+X^2+X+1 1 X^2 X^3+X+1 X^2+1 X X^3+X^2+X+1 X^3 X^3 X^3+X^2+X+1 X X^2+X+1 1 X 1 0 X^3+X^2+1 1 X^3+X^2+1 X^2+X 0 X^2+X X^2+X+1 X^3+1 X^2 0 X^2 1 X^3+X+1 X^3+X^2+X X^2+X 0 X^3+X 1 1 1 X^3+X+1 X^2 X X X^3+X+1 X^3+X X+1 0 0 0 1 X^2+X+1 X^3+X^2+X+1 X^3 X+1 X^3+X+1 X^3+X^2+X+1 0 X^3+X^2+1 X^3+X^2+X X^3+X^2+1 X^2+X 0 X 1 X^3+X+1 X X^3+X X^2 1 0 X^3 X^2+X+1 X+1 1 X+1 X^2+1 X^3+X^2+X+1 X^2+1 X^3+X^2+X+1 X^3+1 X^3+X^2+X+1 X^3 X^3+X^2 X+1 X^3+X^2+X X^3+1 X^2 1 X^3+X X^3+1 0 X^2+X X^2+1 X^2+X X^3+X 1 X^2+X+1 1 1 X^3+X^2+1 X^3 X^3+X 1 X^3+X X^3+X^2+X+1 X^2 X^3+X+1 X^2 X+1 1 X^3 X^3+X^2+X 1 1 X X+1 X^3+X^2+X X^3+1 X^3+X^2+X+1 1 X^2+1 1 X^3+X+1 X^2 X^2+X+1 X X^3+X^2+X+1 X^3+X^2+1 0 X^3+X^2 generates a code of length 84 over Z2[X]/(X^4) who´s minimum homogenous weight is 77. Homogenous weight enumerator: w(x)=1x^0+532x^77+1872x^78+3186x^79+4524x^80+5246x^81+6536x^82+7492x^83+7633x^84+7090x^85+6513x^86+5258x^87+4494x^88+2318x^89+1246x^90+932x^91+341x^92+172x^93+85x^94+24x^95+31x^96+4x^98+4x^99+2x^101 The gray image is a linear code over GF(2) with n=672, k=16 and d=308. This code was found by Heurico 1.16 in 45.6 seconds.