The generator matrix 1 0 1 1 1 X^2+X 1 1 X^2 X 1 1 1 X 1 X^2+X 1 1 1 1 X^2 X^2 1 1 1 0 X^2 1 1 1 1 1 0 X^2+X 1 1 1 1 1 1 1 1 0 1 0 1 1 1 1 1 1 1 1 1 0 1 X 1 1 0 1 X 1 0 X^2 1 1 0 1 1 0 X^2+X+1 1 X X+1 1 1 X^2+X X^2+1 X+1 1 X^2+X 1 X^2 X^2+1 X X+1 1 1 0 X X^2+1 1 1 X^2+X+1 X^2+1 1 X^2 X^2 1 1 X^2 X^2+X+1 0 X^2+X+1 X^2+X+1 X^2+X+1 0 X^2+1 1 X^2+X+1 1 1 X^2+X+1 X^2+X X^2+X+1 X^2+X X X^2+1 1 X^2 1 0 X X+1 X^2+X 1 0 X^2+X X^2+X 1 1 X+1 0 0 0 X 0 X^2+X 0 0 0 X^2 X^2 0 X^2 X X^2+X X X^2+X X X^2+X X X^2 X^2+X X X^2+X X 0 X^2 X 0 X^2+X 0 X^2 X X X X^2+X X^2 0 X X^2+X 0 0 X^2 X^2 0 X^2+X X^2+X X 0 X^2+X 0 X 0 X X 0 X X^2 X^2+X X^2 0 X^2+X X X^2 X^2 X X X 0 0 0 X 0 0 X X^2 X^2+X X 0 0 X 0 X^2+X X^2+X X^2 X 0 X^2+X X^2 X^2+X X 0 X^2+X X X^2 X X 0 X X X^2+X X X^2 0 X^2 0 X^2 X X^2 X^2+X X^2 0 X 0 0 X X X^2 X X X 0 X^2 0 X^2+X X^2 X X^2+X X^2+X X^2 X^2+X 0 X^2+X X^2+X X 0 0 0 0 X^2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 0 0 X^2 X^2 0 X^2 X^2 0 0 X^2 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 0 0 X^2 0 0 X^2 X^2 0 0 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 0 X^2 X^2 X^2 0 0 0 0 0 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 0 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 0 0 0 0 0 0 X^2 0 X^2 0 X^2 X^2 0 0 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 0 0 X^2 0 0 0 0 X^2 0 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 0 0 X^2 0 X^2 X^2 0 0 0 X^2 0 0 X^2 X^2 0 X^2 X^2 0 0 X^2 generates a code of length 67 over Z2[X]/(X^3) who´s minimum homogenous weight is 58. Homogenous weight enumerator: w(x)=1x^0+45x^58+92x^59+232x^60+352x^61+403x^62+572x^63+644x^64+702x^65+778x^66+736x^67+765x^68+728x^69+582x^70+508x^71+326x^72+224x^73+207x^74+114x^75+58x^76+32x^77+30x^78+22x^79+13x^80+10x^81+2x^82+2x^83+9x^84+2x^87+1x^94 The gray image is a linear code over GF(2) with n=268, k=13 and d=116. This code was found by Heurico 1.16 in 4.27 seconds.