The generator matrix 1 0 0 0 1 1 1 1 X^2 1 1 1 X^2+X X^2 X^2+X 1 1 X^2+X 1 X^2 X^2 1 X 1 X^2 0 0 1 1 1 1 1 1 X^2 X^2 1 0 X X 1 X 1 1 1 1 X 1 X^2 1 1 X^2 X^2+X 1 1 1 0 X X^2 X^2 0 1 1 1 X^2+X 1 X^2+X 1 0 1 0 0 0 0 1 1 1 X^2 X^2+X+1 X+1 X^2 1 1 X^2+X+1 0 X 0 1 X^2+X X 1 X+1 1 1 X^2 1 1 X^2+X X^2+X+1 X X+1 1 1 X 1 X^2+X X X^2+1 X^2+X X^2+X X^2+X+1 X^2 X 1 1 1 X^2+1 1 1 1 X^2 X 1 1 1 X 1 0 X^2+X X^2+1 X+1 X^2 X+1 1 X 0 0 1 0 0 1 1 X^2 X^2+1 X^2+X+1 1 X^2 1 0 1 X+1 0 0 X^2+1 X^2+X+1 1 X^2+1 X^2+1 X^2+X X^2+X X 1 0 X^2+X+1 X^2 X^2+1 X^2+X+1 X^2 X^2+X 1 0 X^2+X 1 X 1 X X^2 X^2+X X 1 X+1 X X+1 0 X+1 X X X^2+X X^2+X X^2+1 X+1 X 1 X^2+X+1 0 X^2+1 1 X^2+X+1 1 X X^2+X+1 X^2+X 0 0 0 1 1 1 X^2 X^2+1 1 X X^2+1 0 1 X^2+X+1 X^2 X^2+X X^2+X 1 X^2 X 0 X^2+X+1 1 X^2+1 X+1 X^2 X^2+1 X^2+X 1 X^2+X+1 X^2 X^2+1 X^2+X X+1 X^2+X X^2+X+1 0 X+1 1 1 1 0 X+1 X^2+1 0 1 1 X^2+X+1 X^2+X+1 1 X^2+1 X^2 X^2+X+1 X^2+X X^2 X^2+1 X^2+1 X^2 X^2+1 1 1 X^2+X X+1 X X X^2+X+1 X+1 0 0 0 0 X 0 0 0 0 X X X X^2+X X X 0 X^2 0 X^2+X X^2+X 0 0 X^2 X^2 X^2+X 0 X^2+X X^2+X X X^2+X X^2 X^2+X X^2 X^2 X^2 X^2 X X^2 X X X^2 X X 0 X^2+X 0 X^2 X^2+X X^2 X^2 X^2 X X X^2+X X^2+X 0 0 X^2+X X X^2+X X^2+X X^2 X^2 0 X X 0 0 0 0 0 0 X^2 0 X^2 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 0 X^2 0 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 0 X^2 X^2 0 0 0 0 X^2 X^2 0 0 0 0 0 0 0 0 0 X^2 X^2 0 0 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+258x^58+532x^59+1103x^60+1180x^61+1892x^62+1880x^63+2497x^64+2740x^65+2864x^66+2792x^67+3207x^68+2596x^69+2644x^70+2048x^71+1654x^72+1004x^73+782x^74+484x^75+335x^76+96x^77+120x^78+8x^79+32x^80+16x^82+3x^84 The gray image is a linear code over GF(2) with n=268, k=15 and d=116. This code was found by Heurico 1.16 in 64.8 seconds.