The generator matrix 1 0 0 0 1 1 1 1 X^3+X^2 1 1 X^3 0 X^3 1 1 1 1 1 X^2+X X^3+X X^2 X 1 1 X X^3+X^2+X 1 1 1 1 1 X X^3+X^2 X^2+X X^3+X 1 X^2 X^3+X^2 1 1 1 1 X^3+X^2 1 1 1 X X^2 1 X^2 1 1 1 X^2+X 1 X X^3+X 1 X^3+X^2 X^3 1 X^3+X X^3+X 0 1 0 0 X X^2+1 X^3+1 X^2 1 X^3+X+1 X^3+X^2+X 1 X^3+X 1 X^2+X+1 X^3+1 1 X+1 X+1 1 1 X^3+X 1 X^2+X X^2+X 0 1 X^3+X^2+X X^3+X^2 X^3+X^2+1 X^3+X+1 X^3+X+1 1 X X^3+X^2 X X^3+X^2+X 1 1 0 X^2+X+1 X^2 X^2+1 1 0 X+1 X^3 X X^3+X^2+X X^3+X 1 X^3+X X^2+1 X^3+X^2+X 1 1 1 X^2+X 1 X^3+X X^2 X+1 1 X^3 0 0 1 0 0 X^2 1 X^2+1 1 X^2+1 X^3+1 X^3+X^2+X+1 1 X^2+X X^3+X^2+X X X^2+1 X^2+X+1 X^3+X^2+X X^2 X^3+X^2+X+1 1 X^3+X^2+X+1 X^3+X+1 X^3+1 1 X^3+X^2 X X^3 X^2+1 0 X^3+X^2+1 X^3+1 1 X^3+X^2+X 1 X^3+X^2 X^3+X+1 X^3 X^2+1 X^3+X^2 X^3+X+1 X^3+X^2+1 X^3+X+1 X^2 X^3+X^2+X+1 1 X^3 1 X^3+X^2+X X^3+X^2+X X^3+X^2+1 X X^3+X^2 X+1 X^2+X 0 X^2 X^2+X 1 X^3 X^2+X X^2+X+1 1 0 0 0 1 1 X^2+X+1 X^2 X^3+X^2+X+1 X^2+X+1 X^2+1 X^3+X X^3+X^2+X X^3+1 X+1 X^2+X X^3+X^2+X+1 X^3+X 1 X^3 X^2+X+1 X^3+1 X^3+X^2+X+1 X^3+X X^3+X+1 0 X X^3 X X^3+X^2+1 X^3+X^2+X+1 X^2+X X^3 X^2+1 X^3 1 X+1 X^3+X^2+X X^3+X^2 X+1 X^2 X^3+1 X^3+X^2+X+1 1 1 X^2+X+1 X^3+X^2+X X^3+X^2+X 1 X^3+1 X^3+X^2+X+1 X^3+1 X^3+X^2+1 X^2+X X^3+X^2+X+1 X^3+X X^2+1 X^3 1 X^3+X^2+1 X^3+X+1 1 X^3+X X^3+1 X^2+X+1 0 0 0 0 X^2 0 0 0 0 X^2 X^2 X^3+X^2 X^2 X^2 X^3+X^2 X^3 X^3 X^3+X^2 X^2 X^2 X^3 X^3+X^2 X^2 0 X^2 0 0 0 X^2 X^3+X^2 X^3+X^2 X^3 X^3+X^2 X^2 X^3 X^3+X^2 X^3+X^2 0 X^2 X^3+X^2 0 X^2 X^3 X^3 X^3 X^2 0 0 X^3 X^2 0 X^3 X^3+X^2 X^3 X^3 X^3+X^2 X^3+X^2 X^2 0 X^3 X^3+X^2 X^2 0 X^2 generates a code of length 64 over Z2[X]/(X^4) who´s minimum homogenous weight is 56. Homogenous weight enumerator: w(x)=1x^0+516x^56+1904x^57+4558x^58+7744x^59+14263x^60+19992x^61+29366x^62+33396x^63+37416x^64+34580x^65+30242x^66+20144x^67+13953x^68+7372x^69+4130x^70+1572x^71+569x^72+236x^73+108x^74+24x^75+31x^76+12x^77+10x^78+2x^80+2x^86+1x^92 The gray image is a linear code over GF(2) with n=512, k=18 and d=224. This code was found by Heurico 1.16 in 608 seconds.