The generator matrix 1 0 0 0 0 1 1 1 0 X^2 1 1 X^2+X 1 0 1 X X^2+X X^2+X 1 X 1 X^2 0 0 1 1 1 1 1 0 X 1 1 X^2 1 X^2 1 X^2+X 1 1 X^2+X X^2 1 X 1 0 1 X^2+X 1 1 1 1 X^2+X 1 1 X^2+X 1 X^2+X X^2+X 1 X^2+X X 1 1 1 1 1 0 0 1 0 0 0 0 0 0 X^2 0 0 0 0 X^2 X^2 0 1 1 1 X^2+X+1 1 1 1 1 1 X^2+1 X^2+X+1 1 X^2+X+1 X^2+X X 1 X^2+X X^2+X+1 1 1 X X 1 X^2+X+1 X^2+1 X^2 1 X^2+X+1 0 X^2+X+1 1 X^2+1 1 X X^2+1 X^2+1 X X^2 X^2 X X^2+X 1 0 1 1 X^2+X 1 X X^2+1 X^2+X 0 X^2 X^2+X 0 0 1 0 0 0 1 1 1 1 X^2 X^2+1 1 X^2+X+1 0 X^2+X X^2 X^2+X+1 X^2+1 X+1 X^2+X X X^2+X+1 X+1 X 0 X 1 X^2+X X 1 1 X^2 X^2+X+1 X+1 X+1 1 X^2+1 X X^2 X^2 1 1 1 X^2 X^2+1 1 X+1 X^2+X 1 0 X^2 X^2+X+1 X 0 X^2+X+1 1 X^2+X 1 X^2 1 0 X^2+1 1 X^2+1 X^2+X 1 1 1 0 0 0 1 0 1 1 X^2 X^2+1 X^2+1 X X X 1 1 X^2+X+1 0 X+1 X+1 1 X^2+1 X+1 0 X^2 X^2+X+1 X^2+X+1 X 1 X^2 X^2+X X^2+1 X^2 X^2+X+1 0 X^2+X 0 X+1 X+1 X^2+1 X^2+1 1 X^2 X^2+1 X^2+X 1 X^2+1 1 X^2 X^2+1 X^2+1 X X^2+X X^2+X X X+1 1 X^2 1 X^2+X X 0 1 1 X X+1 X 0 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 X+1 X^2+X+1 0 X^2+1 0 1 X 1 X^2+X+1 X X+1 0 X^2+X X^2+1 X^2+X+1 X X^2+X+1 X^2 X X+1 X^2+X X+1 X^2+1 X 0 X+1 X 1 X 1 X^2 X^2+X 1 X^2+X X+1 X^2+X X X X^2 0 1 X X^2+1 X^2+X+1 X X^2+X 1 1 X^2+X+1 X^2 1 X X X^2+X+1 X X^2+1 0 0 0 0 0 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 0 X^2 0 0 X^2 X^2 0 X^2 0 0 X^2 X^2 0 0 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 0 X^2 0 X^2 0 X^2 0 0 X^2 0 generates a code of length 69 over Z2[X]/(X^3) who´s minimum homogenous weight is 59. Homogenous weight enumerator: w(x)=1x^0+284x^59+661x^60+1272x^61+1840x^62+2414x^63+3209x^64+4050x^65+4827x^66+5264x^67+6007x^68+6004x^69+5675x^70+5522x^71+4900x^72+4190x^73+3340x^74+2450x^75+1517x^76+896x^77+576x^78+296x^79+144x^80+94x^81+57x^82+26x^83+7x^84+4x^85+5x^86+2x^88+2x^89 The gray image is a linear code over GF(2) with n=276, k=16 and d=118. This code was found by Heurico 1.13 in 55.4 seconds.