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 1 1 X 0 1 X X 1 X 1 1 X 1 1 X 1 0 1 1 X^2 1 0 X 1 1 0 1 1 X 1 0 X 0 X 0 0 X X^2+X 0 X^2 X X^2+X 0 X^2+X X^2 X^2+X X 0 X^2 X X^2 X^2+X 0 X^2+X 0 X^2 X^2 X X 0 X X 0 X^2 X X^2+X 0 X^2 0 0 X^2+X X X^2+X X^2+X X^2 X X X^2+X X^2 X^2+X X^2 X^2+X 0 0 0 X^2 X 0 X X X X X^2+X 0 X^2+X X^2+X X^2+X 0 0 0 X X 0 X^2+X X 0 X^2 X X 0 X^2 X^2+X X X^2 X 0 X^2+X 0 0 X^2 X^2+X X 0 0 X X X^2 X^2+X X^2+X X^2 0 X X 0 0 X^2+X X^2+X X^2 X^2 X^2 X^2+X 0 X X X 0 X X^2 0 X X^2+X X^2 X 0 X X X^2+X X^2 X X^2+X X^2+X X X^2+X 0 0 0 0 0 0 X^2 0 0 0 X^2 X^2 X^2 0 0 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 0 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 0 X^2 X^2 X^2 0 X^2 0 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 0 0 0 0 0 0 X^2 0 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 0 X^2 0 0 X^2 0 X^2 0 0 X^2 0 X^2 0 X^2 0 X^2 0 0 X^2 0 0 X^2 0 0 X^2 0 0 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 0 0 0 0 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 0 0 0 X^2 0 X^2 0 X^2 X^2 X^2 0 0 0 X^2 0 0 X^2 0 0 0 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 0 0 X^2 0 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 0 0 0 X^2 X^2 0 X^2 0 0 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 0 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 0 0 X^2 X^2 X^2 X^2 0 generates a code of length 68 over Z2[X]/(X^3) who´s minimum homogenous weight is 60. Homogenous weight enumerator: w(x)=1x^0+49x^60+48x^61+81x^62+108x^63+124x^64+160x^65+171x^66+228x^67+207x^68+200x^69+182x^70+130x^71+91x^72+86x^73+45x^74+34x^75+20x^76+14x^77+27x^78+10x^79+20x^80+2x^81+4x^82+2x^83+2x^85+1x^86+1x^110 The gray image is a linear code over GF(2) with n=272, k=11 and d=120. This code was found by Heurico 1.16 in 0.511 seconds.