The generator matrix 1 0 0 1 1 1 X^2+X 1 1 X^2 X 1 X^2+X 1 1 X^2+X X^2+X 1 1 X X 1 1 X^2 1 X 1 1 0 1 1 1 0 0 1 1 0 1 1 1 1 X^2+X 1 X^2 1 1 0 X X^2+X X^2+X 1 X^2+X 1 1 X 1 1 1 1 1 1 0 1 1 1 1 0 1 0 1 0 0 1 1 1 0 X^2 1 1 X^2+1 X^2+X 1 X 1 X 1 0 1 X^2 1 X 1 1 1 X^2+X+1 X^2 1 X X+1 X+1 1 X^2+X 0 X^2+X+1 1 X^2 X+1 0 X^2+X 1 X^2+X+1 1 X 1 1 X^2+X 0 1 X+1 1 X 1 0 X+1 1 X X^2 X X^2 1 X^2 X^2 X^2+1 X^2+X 1 X+1 0 0 1 1 1 0 1 X+1 0 1 X^2 0 1 X^2+1 X+1 X^2+X+1 1 X^2+X 0 X 1 X+1 X+1 X^2+X+1 X+1 X X^2+X X X^2 X 1 X^2+X 0 1 X^2+X 0 1 X^2+X 1 X^2+X+1 1 0 X^2 0 X^2+1 X+1 X^2+1 1 1 X^2 X^2+1 X^2 0 X+1 1 X X+1 X+1 X^2+X 1 X^2+1 X 1 X^2 X^2 X^2 X^2+X+1 0 0 0 0 X 0 0 0 X^2 X X^2+X X X X X^2+X 0 0 X^2+X X^2+X X^2 X^2 X^2 X X^2+X X X^2 X^2+X 0 X^2+X 0 X^2 X^2 0 X 0 X X 0 0 X^2 X 0 X^2+X X^2 0 0 X^2 X X^2 X^2+X X X^2+X X X^2+X X^2+X 0 X^2+X 0 0 0 X^2 X^2+X X X^2+X X X^2 0 X^2+X 0 0 0 0 0 X 0 0 0 0 0 0 0 0 X^2+X 0 0 0 0 0 0 0 X^2+X 0 0 X^2+X X^2+X X X X^2+X X X^2 X^2 X X^2+X X^2 X^2+X X^2+X X X^2 X^2+X X X^2+X X^2 X X X^2 X^2 X^2 X^2 X^2+X X^2+X X^2 X X^2+X X^2 X X^2 X^2+X X^2+X X^2 X^2+X X 0 0 X^2 0 X X 0 0 0 0 0 X X^2+X X^2 X^2 X X^2 X X^2 0 X^2+X X^2 X X^2 X^2+X X^2+X X X X^2+X X^2 X^2+X X^2 X 0 X^2+X X^2 X^2+X X^2 X X^2+X X X X^2 X^2+X X X^2 X^2+X 0 0 0 X^2 X^2 0 0 X^2 0 0 X^2+X X^2+X X^2 0 X^2 X^2 0 X X^2+X X^2+X 0 X^2 X X^2+X 0 X^2 X^2+X generates a code of length 68 over Z2[X]/(X^3) who´s minimum homogenous weight is 58. Homogenous weight enumerator: w(x)=1x^0+152x^58+204x^59+721x^60+744x^61+1430x^62+1444x^63+2300x^64+1940x^65+3008x^66+2672x^67+3309x^68+2908x^69+3112x^70+2216x^71+2239x^72+1404x^73+1210x^74+596x^75+574x^76+156x^77+250x^78+36x^79+92x^80+16x^81+18x^82+12x^84+4x^86 The gray image is a linear code over GF(2) with n=272, k=15 and d=116. This code was found by Heurico 1.16 in 50.1 seconds.