The generator matrix 1 0 0 0 0 1 1 1 0 1 X^2 1 1 1 1 X X^2+X 1 1 X^2+X 1 X^2+X X^2+X X^2 1 0 X^2 1 1 X 1 0 1 1 1 1 X^2+X 0 1 1 1 1 1 X^2 X^2+X 1 X^2 1 X^2+X X X^2 X^2+X X^2 X^2 X^2+X X 1 0 X^2 1 1 1 0 1 X X 1 1 0 1 0 0 0 0 X+1 X X^2 X+1 1 X^2 X^2+1 X+1 X^2+X+1 1 1 X^2+1 X^2 1 X X^2 X^2+X 1 X^2+1 1 0 1 0 1 X^2 1 X X^2+X X^2+X X^2+X X^2 X^2 X^2+X+1 X^2+X+1 X^2+1 X^2+1 X^2+X+1 X^2+X 1 X 0 X^2 1 1 1 1 0 1 1 1 X+1 0 1 X+1 X^2+1 X^2+1 X X X^2 X^2+X X^2+X 0 0 0 1 0 0 0 1 X+1 1 X^2+1 X^2 X^2+1 X^2+X X^2+X+1 X^2+X 1 X^2+X+1 X^2+X+1 0 X^2+1 X+1 1 X X^2+X X^2 X^2+X 1 X X^2+1 X+1 X X^2+1 0 X^2+1 0 X+1 1 X^2 X+1 0 X+1 X^2+X+1 0 1 X^2 X^2+1 1 X^2+X+1 X^2+X+1 0 X+1 X X^2 X^2 X 1 1 1 1 X^2+X+1 X^2+1 X^2+X 0 X^2+X 1 1 X^2+X 0 0 0 0 1 0 1 X^2 X^2+1 1 X+1 X^2+1 X^2+X X^2 X^2+1 X^2+X+1 X^2+X+1 0 X^2+X X^2+X+1 X^2 X+1 1 1 X 0 X+1 0 X+1 X^2 X^2+1 X^2 X 0 X^2+X X^2+X+1 1 0 X^2+X X^2 X^2 X+1 X^2+X X^2+X+1 X^2+X X^2+1 X X+1 1 X^2+X+1 X+1 X+1 X 1 X^2+X X^2+X X^2+1 X^2+1 X^2 1 X 0 0 1 X^2+X+1 X^2+X X^2+1 X^2 0 0 0 0 0 1 1 X^2+1 X X+1 X^2+1 X^2+X X^2+1 0 X^2 X^2+X+1 1 X^2 X 0 X^2+X+1 X^2+X+1 X X+1 X^2+1 1 X+1 1 X^2+X 0 0 X^2+X+1 0 X X^2+X+1 X^2+1 1 1 1 X+1 1 X^2+1 X^2 X+1 X X+1 0 X^2+X+1 X X+1 X^2 X^2 X^2+X+1 0 1 X^2 X^2+X X^2+X+1 X^2 0 X^2+1 X X^2 X^2 X^2 X^2+X X^2+X 1 0 0 0 0 0 0 X 0 X X X^2+X X X^2 0 X X^2+X X^2+X 0 X^2 X^2+X 0 X^2+X X^2+X X^2+X 0 X^2 X X^2 X X X^2 X X X^2+X X^2+X 0 0 X X X^2+X X^2 X^2 X^2+X 0 X^2+X X^2 0 0 X^2 X X^2 0 0 X^2+X X^2+X X^2 X^2 X^2 X^2+X X^2 X X^2 X^2 0 X 0 X^2+X X^2 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+300x^57+865x^58+1496x^59+2120x^60+3280x^61+4793x^62+6394x^63+7599x^64+9066x^65+11227x^66+12124x^67+12003x^68+11894x^69+11465x^70+10012x^71+8076x^72+6130x^73+4295x^74+3184x^75+2033x^76+1186x^77+745x^78+366x^79+193x^80+72x^81+49x^82+20x^83+12x^84+8x^85+1x^86+4x^87+2x^88 The gray image is a linear code over GF(2) with n=272, k=17 and d=112. This code was found by Heurico 1.13 in 210 seconds.