The generator matrix 1 0 1 1 1 X^2+X 1 1 X^2 1 X 1 1 1 0 0 1 1 X^2+X X^2+X 1 1 1 1 1 1 X^2+X 1 X 1 1 1 0 1 1 1 1 X^2 X^2+X 1 1 X^2+X 1 1 1 0 1 1 1 1 1 1 1 X^2+X 1 1 X 1 1 0 X^2 0 0 X^2 1 1 X^2 1 0 1 1 X^2+X X^2+X+1 1 0 X+1 1 X 1 X^2+1 1 X^2+X 1 1 0 X^2+X+1 1 1 X^2 X^2+X X+1 X^2+1 X X+1 1 X^2+1 1 X^2+1 X^2+X 0 1 X^2 1 X^2+X X^2+X 1 1 X^2+X+1 1 1 X^2 1 X^2+X 1 1 X+1 X X^2+1 1 X^2+X X^2+1 1 X+1 X^2 0 X^2+X 0 1 1 1 1 1 X^2+X X^2+X X 0 0 0 X 0 X^2+X 0 X^2+X X^2 X X X^2+X 0 X X^2 0 X^2+X 0 X X^2+X X^2 X X 0 X^2 X X^2 0 X^2+X X X^2 0 X^2 0 X^2+X X^2+X X^2+X X^2+X X X X 0 0 0 X^2+X X^2 0 0 X^2 X^2+X 0 0 X^2 X^2 X X^2+X X^2 X X X X X X^2 0 X^2 0 0 X 0 0 0 0 X^2 0 0 0 X^2 X^2 0 0 0 0 0 0 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 0 X^2 0 0 0 0 0 0 X^2 X^2 X^2 0 X^2 0 0 X^2 0 0 X^2 X^2 0 0 0 0 0 X^2 0 0 0 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 0 0 0 0 0 X^2 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 X^2 0 0 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 0 0 0 0 0 0 0 X^2 0 0 0 X^2 0 X^2 0 0 0 0 0 0 0 X^2 0 X^2 0 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 0 0 0 0 0 X^2 X^2 X^2 0 X^2 0 X^2 0 0 X^2 X^2 X^2 0 X^2 0 0 0 0 0 0 0 X^2 0 X^2 0 0 0 X^2 0 0 X^2 0 X^2 0 0 X^2 0 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 0 0 X^2 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 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+43x^60+112x^61+157x^62+250x^63+298x^64+342x^65+343x^66+340x^67+395x^68+342x^69+378x^70+346x^71+235x^72+200x^73+117x^74+68x^75+42x^76+24x^77+18x^78+10x^79+6x^80+2x^81+6x^82+8x^83+4x^84+2x^85+3x^86+2x^87+2x^90 The gray image is a linear code over GF(2) with n=272, k=12 and d=120. This code was found by Heurico 1.16 in 1.07 seconds.