The generator matrix 1 0 0 0 1 1 1 1 X^3 1 X 1 1 X^3+X X 1 X^2+X 1 1 1 0 1 1 1 X^2+X X^2 X^3 1 X X^2+X 1 1 0 1 1 1 X^2 X^3+X^2 X^3+X^2+X 1 1 X^2+X 1 X X^3+X^2 1 X^3 X 1 1 X^3+X^2 1 1 X^3+X 1 1 X X^3 X^3+X^2 X X^3+X^2+X 0 1 1 1 0 1 0 0 X X^2+1 X^2+X X^3+X^2+X+1 1 X^2+X X^2 1 X^2+X+1 1 1 X^3+X X X^2 X^3+X+1 X^3+1 1 X+1 X^3+X^2+X+1 X^3+X^2 X^3+X^2 1 X^3 X^2 1 1 X^3 X^2+1 X^2 X^3+1 X^3+X^2+1 X^3+X X^3+X 1 1 X^3+X^2+X+1 X^3+1 1 X^3+X X^3+X^2 1 X^3+X^2+X+1 X^3+X^2 X^2+X X^2+1 X^3 1 X^2 X^3+X^2+1 X 0 X+1 1 X^2+X X^2 X^3+X 1 1 X^3+X^2+1 X^3+X+1 0 0 0 1 0 0 X^3 X^3+X+1 X+1 X^3+X+1 1 1 X^3+1 X^2 X^3+X^2+X+1 X^3+X^2 X^3+X^2+X 1 X^2+1 X^3 X X^2 X+1 1 X^3+X 1 X^2+X+1 X X^2+X+1 X^2+X X^3+1 X^3+X^2+1 X^2+X+1 1 X^3+1 1 X 1 X^3+X X^2+X+1 X^3+X^2 X^3+X^2 X^3+X^2+X X^3+X+1 X^3+X^2+X 1 X^3+X^2+X 1 1 0 X+1 X^2 X^3+X^2+X+1 X^3+X^2 1 X X^3+X^2+X X^3+X^2+X+1 X^3 1 1 X^3+X^2+1 X X^2+X+1 X^3+X^2+X 0 0 0 0 1 1 X^3+X+1 X^2+X+1 X^2+1 X X X^3+X^2+X+1 0 X^3+X X+1 X^3+X^2+1 X^3+X^2 X^3 X^3+1 X^3 X^3+X^2+1 X^3+1 X^3+X^2+X X^3+1 X^3+X^2+X+1 1 X^3+X^2 1 X X^2+X X^3+X^2+X+1 X+1 X^3+1 X^3+X^2+X+1 X^3+X^2+X X^3+X^2+X+1 X^3+X+1 X X^3+X+1 0 X^3+X^2+1 X^3+X^2 X^3 X 1 X^2 X^3+X X 1 X^3+X^2+1 X^2+X+1 X^2+1 X^2+X+1 X^3+X X+1 X^3+X X^3+X+1 X^3+X 1 X^3+X+1 X+1 X^3+X^2+X X^2+X X^2+X+1 X^2+X 0 0 0 0 0 X^3 X^3 X^3 X^3 0 X^3 0 X^3 X^3 0 0 X^3 0 X^3 X^3 X^3 0 X^3 X^3 0 X^3 X^3 X^3 0 X^3 X^3 0 0 X^3 0 0 X^3 X^3 X^3 X^3 0 0 0 0 X^3 0 0 X^3 0 X^3 0 X^3 X^3 X^3 X^3 X^3 0 X^3 X^3 0 0 0 X^3 X^3 X^3 0 generates a code of length 65 over Z2[X]/(X^4) who´s minimum homogenous weight is 57. Homogenous weight enumerator: w(x)=1x^0+84x^57+1070x^58+2416x^59+4517x^60+7152x^61+10459x^62+13966x^63+17332x^64+17202x^65+17215x^66+14450x^67+10549x^68+6814x^69+4231x^70+2008x^71+991x^72+362x^73+139x^74+52x^75+46x^76+2x^77+6x^78+2x^79+4x^80+2x^83 The gray image is a linear code over GF(2) with n=520, k=17 and d=228. This code was found by Heurico 1.16 in 144 seconds.