The generator matrix 1 0 0 1 1 1 X^3 0 X^3 X^2 1 1 1 1 X 1 1 X^3+X 1 1 X 1 X^2+X X^2+X 1 1 X^2 1 1 X^3+X 1 1 1 1 0 X X^2+X 1 X^3+X^2+X 1 1 1 X^2 1 X^3+X^2 X^2+X 1 1 X^2 1 X^3 1 1 X^3 0 X X 1 1 1 X X^3+X^2 1 1 1 1 1 1 1 X^2 1 1 1 X 0 1 X^3+X^2 1 X^3+X 1 1 X X^3 X^2+X 1 1 1 0 1 0 0 X^3+X^2+1 X^2+1 1 X^3+X^2+X 1 1 X^2 X^3+X^2 X^3+1 X^3+1 X^2+X X^3+X X 1 X^3+X+1 X^2+X+1 1 X 1 X^2 X+1 X^3+X^2+X+1 1 X^3+X^2+X X^2 1 X^2+X X^2+X+1 X^3+X+1 X^2 1 X^3+X 1 X^2+1 1 X^3+1 X^3+X^2+1 X 1 X+1 1 1 X^3 X^2+X 1 X^2 X^3+X^2 X^3+X^2+X X^3+X^2 1 X^3+X^2 1 1 X^3+X^2+1 X^3+1 X^3 X^3 1 X^3+X+1 X^3+X^2+1 X^2+X X^3+X^2+X X^3+X^2+X+1 0 X^3+X^2+X 0 X^3+X^2 X^3+X^2+X X^2 0 1 X^3+X+1 1 X^3+X+1 X^2+X X^3+X^2+1 X^3+X^2+X X 1 1 X^3+X^2+X+1 X^3+X^2 X^3 0 0 1 X+1 X^3+X+1 X^3 X^2+X+1 1 X^2+X 1 X^2+X X^3+1 X^3+X^2+1 X 1 X^3+X X^2+X+1 X^2+X+1 X^2 X^3+X+1 X^3+X X^2+1 X^3+X^2 1 X^3+1 X^3+X X^3+X^2+X+1 X^2 0 X^3+1 X^2+X X^3+X X^2+X+1 1 X^3 1 0 X^3+1 X^2+1 0 X+1 X^2+X+1 1 X^3 X^3+X^2 X^3+X^2+X+1 X^3+X^2+X X^3+X^2+1 X X^2 1 X^2+X+1 X^3+X^2+X+1 X^3+X+1 1 X^3+X^2+X X^2 X^2+X 1 X 1 1 X^3 X+1 X^3+1 X^2+1 X^2+X+1 X^2 X^3+X^2+X+1 1 X^2+1 X+1 1 1 X^3+X^2+1 X^3+X^2+X X^3 0 1 X X^3+X^2 1 X^3+X^2+X X^3+X X^2+1 X+1 X^2 0 0 0 X^2 X^2 0 X^2 X^3+X^2 X^3+X^2 0 X^2 0 0 X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^3 X^3+X^2 X^3 0 X^2 0 X^3 X^2 X^3+X^2 X^3+X^2 X^3 0 0 X^3 0 X^3+X^2 X^2 X^3 0 X^2 X^3 X^2 X^3 X^3 X^3+X^2 X^2 X^3+X^2 X^3 0 X^3 X^3 X^2 X^3 0 X^3+X^2 0 X^2 X^2 X^3 0 X^3 X^3 X^3 X^2 X^3 X^3+X^2 X^3+X^2 X^2 X^3 X^3+X^2 X^3 X^3+X^2 X^3+X^2 X^2 X^3 X^2 X^3 X^3+X^2 X^3 X^3+X^2 0 X^2 X^3 X^2 0 X^3 X^2 X^3 0 generates a code of length 87 over Z2[X]/(X^4) who´s minimum homogenous weight is 81. Homogenous weight enumerator: w(x)=1x^0+182x^81+813x^82+1220x^83+1863x^84+1746x^85+1955x^86+1874x^87+1857x^88+1346x^89+1220x^90+788x^91+572x^92+344x^93+310x^94+142x^95+61x^96+24x^97+44x^98+8x^99+5x^100+6x^101+1x^102+1x^104+1x^106 The gray image is a linear code over GF(2) with n=696, k=14 and d=324. This code was found by Heurico 1.16 in 20.1 seconds.