The generator matrix 1 0 0 0 1 1 1 0 1 X X X^2+X 1 1 1 1 0 1 X^2 1 1 1 X^2+X 0 1 1 1 1 X^2+X X^2+X X^2 1 X^2+X 0 X^2+X 1 1 1 0 1 1 X^2+X X^2 X X^2+X 1 1 X^2+X 1 0 X^2 1 1 1 1 X 1 1 0 0 X^2 1 X^2 1 X^2 1 1 1 0 1 0 0 0 1 1 1 X^2 X^2+X 1 1 X^2 X^2+1 X^2+X+1 X^2 0 X^2+X 1 1 X^2+X+1 X+1 1 1 X^2 X^2+X 1 0 X 0 1 1 1 1 X X+1 1 X^2+X 1 X^2+1 1 1 X 1 0 X X+1 X^2 X^2 1 1 X 0 X^2+X+1 X^2 X 0 X X^2+X 1 0 X^2+1 1 X+1 1 0 X+1 0 0 0 1 0 1 1 X^2 X^2+1 X^2+X+1 1 X^2 1 X X^2+1 0 X^2+1 1 1 X X+1 X^2+X X^2 X^2 X^2+1 X^2+X X^2+X X^2+1 1 0 1 X^2+1 X^2+X X+1 X 1 1 X^2 1 X^2+X+1 X^2+1 0 X^2 1 X^2+1 1 1 X^2+X+1 X^2+X 0 X^2 0 X X^2+X X^2+X X^2+X 1 X+1 0 1 0 1 0 X^2+1 X 0 X^2 1 0 0 0 0 1 1 0 X^2+1 1 X^2 1 X+1 X X+1 1 X^2 X+1 X 0 0 0 X+1 X^2+X X+1 X^2+1 X^2+X+1 0 X^2+X+1 X^2+X 1 X^2+X+1 X 1 X+1 X+1 X^2+X X^2 X^2+X 1 X^2+1 X X^2+X+1 X^2+X 1 X^2 1 X^2+X+1 1 1 X+1 X^2+1 X+1 X^2+X+1 X^2+1 X+1 X^2 X X^2+X X^2+X 0 X^2 X^2+X X^2+1 X^2+1 1 1 1 X^2+X 0 0 0 0 0 X 0 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X X^2+X X^2+X X^2+X X^2+X X X^2+X X X^2+X X^2+X X X^2 X^2+X X^2 X^2 X^2+X X^2+X X^2 X X^2+X 0 0 X^2+X 0 X^2+X 0 0 X 0 X X^2 X^2+X X^2 X X X^2 X X 0 X 0 X X^2 0 X^2 X^2+X X 0 0 0 0 0 0 0 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 0 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 X^2 0 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 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+49x^58+258x^59+594x^60+972x^61+1363x^62+1708x^63+2051x^64+2306x^65+2602x^66+2852x^67+3034x^68+3124x^69+2757x^70+2452x^71+2092x^72+1602x^73+1174x^74+706x^75+420x^76+286x^77+204x^78+72x^79+28x^80+28x^81+7x^82+16x^83+4x^84+2x^85+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 44.8 seconds.