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 1 X 1 X^2 1 1 1 1 1 X 1 1 X 1 0 1 X 1 0 X^2 1 1 1 X X^2 0 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 X^2+X X X X^2+X X^2+X X 0 X^2 X X^2 0 X^2+X X^2 0 X^2+X X^2+X X X X 0 X 0 X X X X^2 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 X^2 X^2 X^2+X X^2 0 X^2 X X^2 X X^2 X^2 0 X^2+X X X^2 X^2 0 X^2 X^2+X X X^2+X X^2 X X 0 X^2+X 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 X^2 0 0 0 X^2 X^2 0 X^2 0 X^2 X^2 0 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 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 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 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 X^2 0 X^2 X^2 X^2 0 X^2 0 0 0 X^2 X^2 X^2 0 X^2 X^2 0 0 0 0 X^2 0 0 X^2 0 0 X^2 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 0 X^2 X^2 0 0 0 X^2 0 X^2 0 0 0 0 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 0 X^2 X^2 generates a code of length 67 over Z2[X]/(X^3) who´s minimum homogenous weight is 60. Homogenous weight enumerator: w(x)=1x^0+150x^60+8x^61+122x^62+88x^63+154x^64+256x^65+112x^66+336x^67+132x^68+232x^69+92x^70+88x^71+126x^72+16x^73+48x^74+58x^76+10x^78+14x^80+4x^84+1x^112 The gray image is a linear code over GF(2) with n=268, k=11 and d=120. This code was found by Heurico 1.16 in 1.08 seconds.