The generator matrix 1 0 0 0 1 1 1 X^2 1 1 X^2+X 1 1 X^3+X^2 X^2+X 1 1 1 0 X^3+X^2 1 X^2 X X^2 1 1 1 X^3 1 X^2+X 1 1 X^2+X X^3+X^2 X^2+X 1 X X^3+X 0 1 0 1 X^3+X X 1 1 1 1 1 1 1 X 1 1 1 X^2+X X^3 X^2+X X^2 1 1 X^3+X 1 1 1 0 1 0 0 0 X^3+1 X^3+1 1 X^3+X^2+X X^3+X X^3+X^2+X X+1 X^3+X^2+X+1 1 1 X^2+1 0 X^3 X X^2+X X^3+X^2+1 1 1 X^2 X^3+X^2+X+1 X^2+X+1 X 1 X^2 1 X^3+X^2+X+1 X X^3+X^2 1 X^3 X^3+X^2+X X^3+X X^3+X^2 1 X^3+X^2+X+1 1 X^3+X^2+X+1 1 0 0 X^3+X+1 1 X^2+1 X+1 X^3+X^2+X X^3+X^2 1 X^3+X^2+1 X^2+X X^3+1 1 1 1 X 1 X^3 X^2 X^3+X^2+1 X^3+X 0 0 0 1 0 1 1 X^2 X^2+1 0 X^3+1 1 X^2+1 X^2+X X^3+X^2+X+1 X^3 X^2 1 X 1 1 1 X X^2+1 X 1 X^3+X^2+X X^3+X^2+X+1 X^2+X X^3 1 X^3 0 1 X^2+1 1 X+1 1 X^2 X^2 X^2+X+1 X^3 X^2+X+1 X^3+X^2+X+1 1 X^3+X^2+X X^3+X^2+X X^2 X^2+1 X^2+X X^2+1 X^3+X^2+X+1 X^2+X X^3+X 0 X^2+X+1 X+1 X^2+X+1 X^3+X^2 1 X+1 X^3+X X^2+X 1 0 0 0 0 0 1 1 X^2 X^2+1 1 X^2+X+1 X^3+X X^2+1 X^2+1 X^2+X X^3+X^2+X X^2+1 X^2+X+1 X^3+X^2+X+1 X^3+1 X^3+X^2+X+1 0 X^3+1 X+1 X^2+X 1 X 0 X^3 X^3+X^2 X^3+X+1 X^3+X^2+X+1 X^3+X X^2+X X^3+1 X^3+X+1 X X^3+X+1 X^3+X+1 1 X^3+X^2+X X^3+X+1 X+1 X^3+X X X^3+X+1 X^2+X X^3+X^2+X+1 X^2+X+1 X^2+X X^3+X^2 1 X^3+1 X^3+1 X^3+X X^3 X^2 1 X+1 X^3+X^2+1 X+1 X^2+X X+1 1 X^3+X^2+X X^2+1 0 0 0 0 0 X^3+X^2 0 X^3+X^2 0 X^3 X^3 X^3 X^3 X^3 X^3 0 0 X^3 0 0 X^3 X^3 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^3+X^2 X^2 X^3+X^2 X^3 X^2 X^3+X^2 X^3+X^2 X^2 X^3+X^2 X^2 X^2 X^3 X^3+X^2 0 X^3+X^2 X^3+X^2 X^3+X^2 0 X^2 X^2 X^3 X^3+X^2 0 X^3 X^3 X^3+X^2 X^3 X^2 X^3 X^2 0 generates a code of length 65 over Z2[X]/(X^4) who´s minimum homogenous weight is 56. Homogenous weight enumerator: w(x)=1x^0+83x^56+806x^57+2382x^58+4546x^59+8143x^60+13650x^61+20181x^62+28978x^63+33935x^64+36556x^65+33742x^66+29102x^67+20798x^68+14048x^69+8194x^70+3990x^71+1663x^72+736x^73+346x^74+162x^75+43x^76+26x^77+17x^78+4x^79+6x^80+2x^81+2x^82+2x^83 The gray image is a linear code over GF(2) with n=520, k=18 and d=224. This code was found by Heurico 1.16 in 556 seconds.