The generator matrix 1 0 0 0 0 1 1 1 0 X^2 1 1 1 0 0 1 X^2 1 1 1 1 1 X^2+X 1 1 X X X^2 X 1 0 X^2 X^2+X 1 X^2+X 0 X X^2 X^2 1 1 X^2+X 1 1 1 X 0 1 0 1 1 1 1 1 1 X^2+X X^2+X 1 X^2 1 X^2+X 0 X^2 1 0 1 1 0 1 0 0 0 0 0 0 X^2 0 0 X^2 0 0 X^2 X 1 X^2+1 X+1 X^2+X+1 X+1 1 1 1 X+1 1 1 1 1 X^2+X X^2+X X 1 X+1 0 1 1 1 X^2+X X 1 1 X X^2 X^2+1 X 0 X+1 1 X^2+X X^2 1 X^2+X+1 X^2+X X X^2 X^2+X X^2+X+1 1 X^2 1 1 1 X^2 1 X^2+X X 0 0 1 0 0 0 1 1 1 1 X^2 X^2+X+1 X+1 1 X X X^2+X+1 X+1 X^2+X X^2+X X^2 X^2+X X^2+X+1 X^2+X+1 X+1 X^2+1 X^2+X X^2+X+1 X^2+X 0 1 1 0 X^2+1 1 X X^2 X^2+1 1 X X^2+X+1 1 0 X+1 X X 1 X^2 X^2+X X X X^2+1 X^2+X+1 X+1 1 X X X^2+X X^2+1 X^2+1 X+1 1 X+1 X^2 X^2 X+1 0 0 0 0 1 0 1 1 X^2 X^2+1 X^2+1 X 1 X X^2+X 1 X+1 X^2+X X^2+1 X^2+X 1 X^2+1 X^2+X X^2+X+1 1 0 X+1 X^2+1 0 X^2+1 X^2+X X+1 1 0 X^2 0 X X^2+X+1 X+1 X^2 X^2+1 X^2+X X X^2+X+1 X+1 X^2+1 0 X^2+X+1 X^2+X+1 X^2+1 X^2 0 X X^2+1 X^2 X^2+1 1 1 0 0 X^2+X X^2+X+1 X^2+X+1 0 X^2+1 X^2 X^2+X+1 X^2+X 0 0 0 0 1 1 X^2 X^2+1 X^2+1 X X^2+X+1 X^2+X+1 0 X+1 X+1 X^2 X X^2+1 X X+1 X X^2+1 X^2+X+1 X^2 X^2 X^2 0 X^2+X+1 X+1 X^2 1 X^2+X X^2+1 X^2+X+1 X^2 X 0 X^2+X+1 X^2+X+1 X^2+X 0 X^2 X^2+X+1 X X^2 1 X^2+X 1 1 X^2+1 X^2+X 0 X X^2+X X^2+X+1 X+1 X+1 X X 1 X^2+1 X^2+1 X^2+X+1 X^2 X^2+1 X X^2+X+1 0 0 0 0 0 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 0 X^2 0 X^2 0 X^2 X^2 0 0 0 0 X^2 X^2 0 X^2 0 0 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 0 0 X^2 0 X^2 0 0 0 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 0 X^2 generates a code of length 67 over Z2[X]/(X^3) who´s minimum homogenous weight is 57. Homogenous weight enumerator: w(x)=1x^0+184x^57+683x^58+1252x^59+1717x^60+2522x^61+3422x^62+3670x^63+4533x^64+5466x^65+5893x^66+6392x^67+6096x^68+5686x^69+5003x^70+4148x^71+3092x^72+2052x^73+1590x^74+972x^75+555x^76+318x^77+135x^78+70x^79+34x^80+26x^81+10x^82+8x^83+4x^84+2x^85 The gray image is a linear code over GF(2) with n=268, k=16 and d=114. This code was found by Heurico 1.13 in 53.9 seconds.