The generator matrix 1 0 0 0 0 1 1 1 0 1 X^2 1 1 X X^2 1 X 1 1 X 1 1 X 1 X^2+X X X^2+X 1 X^2+X 1 1 1 0 X^2 0 1 1 1 1 1 1 1 1 0 1 1 1 X^2 X^2 X^2 X^2+X X^2+X 1 0 1 0 X X^2+X 1 1 1 X^2 1 1 0 1 0 0 0 0 X+1 X X^2 X+1 1 X^2 1 1 1 X X^2+X 1 1 X^2+X 0 X^2 X^2 X^2+1 1 1 1 X^2+X 1 X^2+X+1 X+1 X+1 X^2 X X^2+X X 0 X^2 1 1 X^2 X^2+1 X+1 1 X^2 X^2+X+1 X^2+1 X^2 1 1 0 0 X^2+X 1 X 0 X 1 X^2+1 1 X 1 0 X^2+X 0 0 1 0 0 0 1 X+1 1 X^2+1 X^2 X^2+1 1 X^2+1 1 X^2+X+1 1 1 X 1 X^2+X+1 0 X^2 X^2+X 0 X^2+X X^2+1 0 X^2+X+1 0 X^2+X X 1 X^2+X 1 X^2 0 X^2+1 X^2+X X+1 X^2+X 1 X+1 X+1 X^2+X+1 0 X^2+X+1 1 1 1 X^2+X X X+1 1 X^2+X 0 0 X X+1 X^2 X^2 X 0 X^2+X 0 0 0 1 0 1 X^2 X^2+1 1 X+1 X^2+1 X^2+X X X^2+X X+1 X^2+X+1 X^2 X^2+1 0 X+1 0 X+1 1 1 0 X+1 1 X^2 X^2 X^2+X X^2 1 X 1 X^2+X X^2+X+1 0 X^2 X X^2+X+1 0 0 X X^2 0 X+1 X+1 X^2+1 X^2+1 X^2+X X^2+X 1 X^2+X+1 X^2+X+1 1 1 1 X^2 X^2+X 0 X X^2+X+1 X X^2+X 0 0 0 0 1 1 X^2+1 X X+1 X^2+1 X^2+X X^2+1 0 1 0 X^2+X+1 X^2+X+1 X^2 X+1 X^2 X^2+X 0 X+1 X+1 X^2+X+1 1 X+1 X+1 0 X^2+X X^2+1 X^2 X^2+X X^2+X+1 X^2+1 X+1 X+1 0 X^2+X X^2+X+1 X^2+X 0 X^2+1 X+1 X^2+X+1 X^2+X+1 0 X+1 X^2+X 0 1 X^2+X X+1 X^2+X+1 X+1 X^2+X 1 X^2+X X^2+X X X^2+1 0 0 X^2+X 0 0 0 0 0 X 0 X X X^2+X X X^2 X^2 X^2 X^2+X X^2+X 0 X 0 X^2+X 0 X^2+X X X^2+X X^2 X X^2+X X^2 X^2 0 X^2 X^2+X X^2+X X^2 X^2+X 0 X^2+X X X^2+X X^2 X^2+X X^2+X X X^2+X X X^2 0 0 X^2 X X^2+X X^2+X X^2 X^2 0 X^2+X 0 X^2+X X X^2 X 0 X X^2 generates a code of length 64 over Z2[X]/(X^3) who´s minimum homogenous weight is 53. Homogenous weight enumerator: w(x)=1x^0+174x^53+625x^54+1212x^55+1891x^56+3198x^57+4560x^58+6134x^59+7907x^60+9416x^61+11104x^62+12450x^63+12920x^64+12372x^65+11858x^66+10346x^67+7965x^68+6098x^69+4313x^70+2750x^71+1630x^72+1034x^73+562x^74+248x^75+152x^76+88x^77+34x^78+12x^79+14x^80+4x^81 The gray image is a linear code over GF(2) with n=256, k=17 and d=106. This code was found by Heurico 1.13 in 196 seconds.