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 1 X X^2 0 X^2 X^2 1 X^2+X 0 X^2+X 0 1 1 1 1 X X^2 1 1 1 1 1 X X 0 0 1 X^2+X X 1 1 1 0 X X^2 1 1 X 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 X^2+X 1 1 X^2+X X 1 X^2+1 1 X^2 X^2+X 1 X+1 0 X^2+X X^2+X X^2 1 X 1 X^2 X+1 X^2+1 1 X X 1 X X^2+X X^2+X X^2+1 X^2+X+1 X^2 1 X^2 1 X^2+X+1 X 1 0 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 0 X^2+X X^2+X+1 1 1 X^2 X^2+1 X+1 1 1 X X^2+X 1 1 X^2+X+1 1 X+1 X^2+X+1 X^2 0 X^2+X+1 1 X^2+X+1 1 X X^2+1 X^2+X 1 0 X^2+1 X^2 X X+1 X^2 0 X X^2+X+1 X^2+X 1 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 X^2+X X^2+1 0 X+1 1 X^2 X^2+X X^2+1 X X^2+X X^2+X X^2 X+1 X^2+X X^2+1 X^2+X X^2+1 0 X^2+1 X^2+X+1 X^2+X X^2+X X^2+X+1 X^2+X+1 1 X X^2+X X+1 1 1 X+1 X X^2+X+1 1 1 X^2 0 X^2+1 X^2+X+1 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^2+X+1 1 X^2+X X X^2+1 X X^2+1 0 X^2+1 X+1 X+1 X^2+X X 0 X^2+X+1 1 X^2+1 X^2+X 0 X+1 X^2+X X^2+1 X^2 X^2+1 1 X X X^2+X+1 X+1 X^2+1 1 X+1 0 X X^2+1 X X^2+X 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 0 X^2 X^2 X^2 0 0 0 X^2 0 X^2 0 0 0 X^2 X^2 X^2 0 0 0 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 generates a code of length 66 over Z2[X]/(X^3) who´s minimum homogenous weight is 56. Homogenous weight enumerator: w(x)=1x^0+191x^56+664x^57+1213x^58+1690x^59+2484x^60+3176x^61+3855x^62+4810x^63+5322x^64+5988x^65+6295x^66+6118x^67+5769x^68+5022x^69+4144x^70+3068x^71+2280x^72+1502x^73+803x^74+542x^75+283x^76+146x^77+101x^78+26x^79+22x^80+14x^81+5x^82+2x^83 The gray image is a linear code over GF(2) with n=264, k=16 and d=112. This code was found by Heurico 1.13 in 52.5 seconds.