The generator matrix 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X X^2 X X^2 1 X 1 X X^2 1 X 1 1 X^2 1 X^2 X X 1 X 0 1 X 0 1 X^2 X 1 0 X X 1 1 X 0 X 0 0 0 X X^2+X X 0 X^2 X^2 X X^2+X X X 0 0 0 X^2 X^2+X X^2+X X^2 X^2+X X X^2+X 0 0 X X^2 0 X X 0 X 0 X^2 X X X^2+X X 0 0 0 X^2+X X^2+X X^2 X^2 X^2 0 X X X^2+X 0 X^2 X X^2 0 X^2 0 X X X^2+X X^2 X^2 X^2 X X^2+X 0 0 0 X 0 X X X^2+X 0 0 0 X X X 0 X^2 X^2+X X 0 X^2 X^2 0 0 X^2+X X^2 X X^2+X X^2 X^2+X X X 0 X^2+X 0 0 X X X^2+X X X^2 X X^2 0 X X^2 X^2+X 0 0 X 0 X^2+X X^2 X^2 X X 0 0 X X^2 X^2 X^2+X X^2 X^2+X X 0 X^2 X X X 0 0 0 X X 0 X^2+X X X^2 X X^2 0 X X^2 X^2+X X X^2 X^2 X X^2+X X^2 X 0 X X^2+X X^2+X 0 X^2 X^2 X^2+X X^2 X X^2+X X^2 X X X^2 X^2 X^2+X 0 X^2+X X^2+X X^2+X 0 X^2+X 0 0 X^2+X X X^2+X X^2+X X^2 X^2+X 0 X X 0 X X^2 X^2 X^2+X 0 X X^2+X X^2+X 0 X^2+X X 0 0 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 0 0 0 X^2 X^2 X^2 X^2 0 0 X^2 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 0 0 0 X^2 0 0 0 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0 0 0 X^2 0 0 0 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 0 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 0 0 0 0 0 0 X^2 0 X^2 0 0 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 0 X^2 0 0 0 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 0 0 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 0 0 0 0 0 0 0 X^2 0 0 X^2 0 0 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 0 0 X^2 0 0 0 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 0 0 0 0 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 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+137x^58+8x^59+357x^60+60x^61+584x^62+148x^63+759x^64+308x^65+870x^66+484x^67+913x^68+492x^69+794x^70+348x^71+690x^72+156x^73+509x^74+36x^75+270x^76+8x^77+138x^78+70x^80+34x^82+11x^84+4x^86+2x^90+1x^92 The gray image is a linear code over GF(2) with n=272, k=13 and d=116. This code was found by Heurico 1.16 in 6.14 seconds.