The generator matrix 1 0 0 0 1 1 1 0 1 1 1 X 1 0 0 X X X^2+X X 1 X^2+X 1 1 X 1 1 X^2+X 1 X 1 1 X 1 X^2 0 1 1 1 X^2+X X^2+X 1 X 1 1 X^2 1 1 1 X^2 X^2 1 1 X X^2 1 1 1 0 X 1 X^2+X 1 1 1 1 X^2 0 1 0 1 0 0 0 1 1 1 X^2+X+1 X^2+1 X 1 0 1 X X 1 X^2+X 1 X^2+X+1 X^2 X X^2+1 1 X X+1 1 1 1 X^2+X X^2 X^2 X^2+X 1 1 X X^2+1 0 X^2+X 1 X^2+1 1 X^2+X 0 0 X+1 X^2+X+1 X 1 1 1 X X^2+X X^2+X X^2+X+1 1 0 X^2+X 1 X^2+1 1 X^2+X+1 X^2+1 X+1 X^2+X+1 0 1 0 0 0 1 0 1 1 0 1 X^2+1 X^2+X X X^2+1 X+1 0 1 X^2 X+1 1 X X^2 1 X+1 X^2 X X^2+X+1 1 X^2+1 X^2+X+1 X^2+X+1 0 0 0 1 0 X^2+X X^2+X X^2 X^2+1 1 X^2+1 X^2+X X^2 X^2+X X 1 X^2+X+1 X^2+1 X^2+X+1 X 0 X^2+X X^2 1 1 X X X^2+X+1 1 X+1 X^2+1 1 1 X^2+1 X+1 0 1 X 0 0 0 0 1 1 0 1 X^2+1 X^2+X+1 X^2 X^2+X+1 0 X^2+X X+1 X+1 1 X^2 1 X^2 X^2+X+1 X^2+X 1 X^2+X 1 X^2 X^2+1 X^2+X 0 X^2+1 X^2+X X^2+1 1 X^2+X+1 1 X^2 X^2+1 X+1 X X^2+X+1 X^2+X X X X^2 X^2+1 X X X^2+X+1 X^2+X X^2+X+1 0 1 0 0 X^2+1 X+1 X^2+1 X^2+1 X 1 0 X+1 1 1 X 0 X^2 0 0 0 0 0 0 X^2 0 0 X^2 X^2 0 0 X^2 X^2 0 X^2 0 X^2 X^2 0 0 X^2 0 X^2 X^2 0 0 0 X^2 0 X^2 X^2 0 X^2 0 0 X^2 0 0 X^2 0 0 0 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 0 0 0 X^2 0 0 0 X^2 X^2 0 0 0 0 0 0 X^2 0 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 0 0 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 0 X^2 0 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 0 X^2 X^2 0 0 0 0 0 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 0 0 X^2 X^2 X^2 0 0 0 0 X^2 X^2 X^2 X^2 0 0 0 0 X^2 0 0 0 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 0 0 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+71x^58+338x^59+543x^60+1052x^61+1249x^62+1914x^63+1652x^64+2714x^65+2435x^66+3148x^67+2592x^68+3344x^69+2257x^70+2744x^71+1866x^72+1816x^73+977x^74+976x^75+451x^76+268x^77+163x^78+92x^79+57x^80+22x^81+13x^82+2x^83+6x^84+3x^86+2x^87 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 44.1 seconds.