The generator matrix 1 0 0 0 1 1 1 1 X^3 1 1 0 1 X^3+X^2 X^3+X 1 X^2+X X^3+X^2+X 1 X^2 X^2+X 1 1 X^2+X X^3+X 1 1 1 1 X^3+X^2 X^2 1 1 1 X 1 1 X^3+X^2 X^3 1 X 1 1 1 1 X^2+X 1 X^3+X^2+X X^3 0 1 1 1 0 1 1 1 1 1 1 1 1 X^3+X^2 X^3+X^2 X^3+X^2+X X X^3+X^2+X 1 0 1 0 0 X X^2+1 X^3+X^2+X X^3+X^2+X+1 1 X^3+X X^3+X^2+1 1 1 1 X^3+X X^2 1 0 X^3+X+1 X^3+X 1 X^2+X X^2+X 1 1 X+1 X^3+X^2+X 1 X^3+1 X^3+X X X^2+1 X^3+X X^3+X^2 X^3+X X^3+X X^3+X^2+1 1 1 X^2+X 1 X^2+X+1 X^2 X+1 X^3+X 1 X^3+X^2+X X^2+X X 1 X^3+X^2+X+1 X^3+X^2+X X 1 X^3+X+1 X^3+1 X^3+X X+1 X^2+X+1 X^3+X^2+1 X^2+X X^2+X+1 1 1 X^2+X 1 X^3+X^2 0 0 0 1 0 0 X^3 X^3+X+1 X^2+1 X^3+X^2+1 X^3+X^2+1 X+1 X^2+X X^2+X X+1 1 X^3+X^2 X^3+X^2+X 1 X^2+X 1 X^3+X^2+1 X X^2+1 X X^2+1 X^3 X^2+1 X^3+1 X+1 X^2+X 1 X^2 X^2+X+1 X^3+X^2+1 1 X^2 0 X^2+1 X^3+X+1 X^2 X^3+X^2+X+1 X^3+X^2+X X^3+X X+1 X X^3+X+1 X^2+X 1 X^3+X^2 0 0 X^2+X+1 X^2+1 X^3+X X^3+1 X^2 X^2+X+1 X^3+X+1 X+1 X+1 1 X^3+X^2+X+1 X^3+X^2 X^2+X+1 X^3+X X^2+1 1 0 0 0 0 1 1 X^3+X+1 X+1 X^2+1 X^3+X X^3+X^2+X X^2 X+1 X^2+X X^2+1 X^3+X^2+1 X^3+X^2+X X^2+1 X^2+X 0 1 X^3 X^3+X^2+1 X+1 X^3+X X+1 X^3+X+1 0 X^3+X^2 X^3+X^2+X+1 1 0 X X^3 X^2+X+1 X^3+X^2+X+1 X^3+X^2 X^3+X^2 X^3+X+1 X^3+X+1 X^3+1 0 1 X^3+1 X^3+X X^2+X+1 X X^3+X^2 X^2 1 X^3+1 0 X^3+X X^2 X^2+X 1 1 X^3+X 1 0 X X^3+X+1 X^2+X X^2+X+1 X^2 1 X^3+X^2+X+1 X^3+X^2+1 0 0 0 0 0 X^3 X^3 X^3 X^3 0 X^3 X^3 0 X^3 0 0 X^3 0 0 X^3 0 0 X^3 X^3 0 0 0 0 0 0 X^3 X^3 0 0 0 X^3 0 0 X^3 X^3 0 X^3 0 X^3 X^3 0 X^3 X^3 X^3 X^3 X^3 X^3 0 X^3 0 0 0 X^3 X^3 0 X^3 0 0 X^3 X^3 0 X^3 X^3 0 generates a code of length 68 over Z2[X]/(X^4) who´s minimum homogenous weight is 60. Homogenous weight enumerator: w(x)=1x^0+206x^60+1102x^61+2561x^62+4930x^63+7277x^64+10774x^65+13361x^66+16648x^67+16810x^68+17208x^69+13797x^70+11024x^71+7184x^72+4540x^73+2009x^74+856x^75+456x^76+186x^77+62x^78+46x^79+14x^80+14x^81+2x^82+4x^84 The gray image is a linear code over GF(2) with n=544, k=17 and d=240. This code was found by Heurico 1.16 in 151 seconds.