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 1 1 1 1 X 0 X^2 0 X^2 X^2 X^2 X^2 1 1 X X X 1 X^2 0 1 X 0 1 X 1 1 1 0 0 1 X^2 1 1 0 X 0 0 0 0 0 0 0 0 X^2 X X X^2+X 0 X^2+X X^2+X 0 X X^2 X^2+X X^2 X X X^2+X X X^2 X^2+X 0 X^2+X 0 X^2 X X^2+X X^2 0 X^2+X 0 X^2+X X^2 X X 0 X X 0 X X X^2+X X^2 X 0 X^2 X 0 X^2 0 X^2+X X^2+X 0 X^2+X X X X X^2+X X X 0 0 0 X 0 0 0 0 0 0 0 X^2+X X^2 X X X X 0 X 0 X X^2+X X^2 0 X^2+X X X^2 X^2+X X^2 X^2 0 0 0 X^2+X 0 X^2+X X^2+X X^2 X^2 X X X^2+X 0 X X X^2 X X^2 X^2 X^2+X X^2+X X 0 X 0 X^2+X 0 X^2 X^2+X X^2+X 0 X^2+X X^2 X X X^2+X X^2 0 0 0 0 0 X 0 0 0 X X^2+X X X X^2+X 0 X X^2 0 X^2+X X^2+X X^2+X X^2 X^2+X X 0 X^2 X^2+X X^2 X^2+X 0 X^2 X X X X X^2 X^2 X^2 X^2+X 0 X^2+X X^2+X X^2 X^2 0 0 X^2+X 0 X^2 X 0 X X^2 X^2+X X X^2 X^2+X X X X X^2 X^2+X X^2+X X^2+X X^2+X X^2 X^2 X X^2+X 0 0 0 0 0 X 0 X X X X^2 X X X X^2 X^2 X^2+X X^2+X X^2 X^2 X^2+X X^2+X X X^2+X X^2 X X X^2+X X^2 X 0 X^2 X^2+X 0 0 0 X^2+X X^2+X X^2 X^2 X^2+X X^2 X X^2 0 0 X X X^2 X 0 X^2 X^2 X^2+X 0 0 0 X 0 X^2 X 0 X X^2 0 0 X^2 X^2+X 0 0 0 0 0 0 X X X^2 X^2+X X^2+X X X X^2+X 0 X X^2 X^2 X^2 X^2+X X 0 X^2 X^2 0 X^2+X X 0 X^2 X^2+X X^2 X X X X X^2 0 X 0 X^2 X^2 X^2 X X^2+X X^2 0 X^2 0 X 0 X X^2+X X^2 X^2+X 0 X^2 0 X^2+X X X X X 0 0 X^2+X X^2+X X^2 X^2+X 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 0 X^2 X^2 0 0 0 0 0 0 X^2 X^2 0 X^2 0 0 0 0 X^2 0 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 0 0 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 0 0 0 generates a code of length 68 over Z2[X]/(X^3) who´s minimum homogenous weight is 56. Homogenous weight enumerator: w(x)=1x^0+57x^56+90x^57+190x^58+262x^59+395x^60+456x^61+549x^62+718x^63+834x^64+1146x^65+1303x^66+1322x^67+1553x^68+1652x^69+1306x^70+1070x^71+880x^72+766x^73+541x^74+354x^75+294x^76+192x^77+164x^78+98x^79+64x^80+46x^81+41x^82+14x^83+18x^84+4x^85+1x^86+2x^87+1x^98 The gray image is a linear code over GF(2) with n=272, k=14 and d=112. This code was found by Heurico 1.16 in 22.8 seconds.