The generator matrix 1 0 0 0 1 1 1 X^3 1 1 X^3 1 X^2 X^3+X^2 1 X^2+X X 1 X^3+X^2 1 1 1 X^2 1 X^2 1 X^3+X 1 X 1 X^2+X 0 1 1 1 X^2 X^2 1 1 X 1 X^3+X^2+X 1 1 1 1 1 0 1 1 1 X^2 1 X^3+X^2+X 1 X^3+X^2+X 1 X^2+X 1 1 0 1 0 1 0 0 0 X^3+1 X^3+1 1 1 X^3+X^2+X 1 X^3+X 1 X^3 X^3+X^2+1 1 X^3+X^2 X^3+X+1 1 X^3+X X^2+X+1 X^2+X X X^3+X^2+X+1 1 X^3+X^2+X+1 1 X^2+X X^2+X X^3+X 1 X^3+X^2+X X^3 X^3+X X^3+X^2+X+1 X^3+X 1 1 X^3 X^3+X X^3+1 1 X^2+1 X^3+X+1 X^3 X X^3+X^2+X+1 1 1 X^2 X^3+X^2+1 1 X^2 X^3 X^2+1 X^2 X^3+X X^3+X^2 X^2+X+1 0 X^2 X^3+X+1 0 0 1 0 1 1 X^2 1 X^3+1 X^2 X^3+X^2+X+1 X^3+X^2+X+1 X^3+X 1 X^3+X^2+X X^3 X^3+X^2+X X^3+X^2 X^2+1 0 X^2+X+1 X^3+1 1 X^3+X^2+X X+1 X^3+1 X X^3+X+1 1 X^2+X X^3 X^3+X^2 X^3+X^2+X X^3+1 X^2+X+1 1 0 0 X+1 0 X^2+X X^3+1 X^3+X^2+1 X^3+1 X^3+X X^3+X^2+X+1 X^3+X^2+X+1 X^3+X^2+1 X^2 X^3+X X^3+X^2+X+1 X^2+X 0 1 X^3 1 X^3+X^2 1 X^2+X 0 1 X^3+X^2+1 0 0 0 1 1 X^2 X^2+1 X^3+1 X+1 X^2+X+1 X^2+X X^2 X^3+X^2+X+1 X^3+X^2+X+1 X^3 X^2+X+1 1 0 X^3+X^2+X X X^2+1 X^3+1 X^2+X X+1 X^3+X^2+1 X^3+X^2 X^3+X^2 X^3+X^2+X X+1 X^3+X^2+X+1 1 1 0 X+1 X^3+X+1 X^3+X^2+X+1 X X^3+X^2+X X^3+X^2+1 1 1 X^3+X^2 X^3+X^2 X^3+X^2+1 X^3+X+1 X^3 X 0 X^3+X^2+X+1 X X^3+X^2 X^3+X X+1 X^3+X^2 X^3+X^2+X+1 X^2+1 X^2 X^2+X+1 X^3+X^2+X X^2 0 X^2+1 0 0 0 0 X^3+X^2 0 X^3+X^2 X^3+X^2 X^2 X^2 X^3 0 X^2 X^2 0 X^2 X^3+X^2 0 X^3 X^3 X^3+X^2 X^3+X^2 0 X^3+X^2 X^2 X^3 X^3 0 X^3+X^2 X^3 X^3 X^3 X^2 0 0 X^3 X^2 X^3+X^2 0 0 X^3 X^2 X^3+X^2 0 0 X^3 X^2 X^3 X^3+X^2 X^3+X^2 X^3+X^2 0 0 X^3+X^2 0 X^2 X^3+X^2 X^3 X^2 X^2 X^2 X^2 generates a code of length 62 over Z2[X]/(X^4) who´s minimum homogenous weight is 54. Homogenous weight enumerator: w(x)=1x^0+444x^54+1716x^55+4424x^56+7432x^57+13640x^58+20628x^59+28364x^60+34228x^61+39416x^62+35092x^63+29405x^64+20524x^65+13522x^66+7084x^67+3636x^68+1548x^69+596x^70+248x^71+142x^72+12x^73+26x^74+12x^76+4x^78 The gray image is a linear code over GF(2) with n=496, k=18 and d=216. This code was found by Heurico 1.16 in 584 seconds.