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 0 1 0 0 1 X 1 1 1 X 1 X 0 X^2 1 X 1 1 1 X 1 0 1 1 0 1 X 1 X 1 X 1 0 X X 0 X 0 X 0 0 X X^2+X 0 X^2 X^2+X X 0 X X X^2 X^2 0 X X^2+X 0 0 X^2+X X^2+X X^2 X^2+X X X^2 X^2 X X 0 X^2+X X 0 X^2 0 X X 0 0 X^2 0 X^2+X X^2+X X X X^2 X X^2 X^2 X^2 X^2 X X 0 X X 0 X^2 X^2 X^2+X X^2 X X X X^2+X X^2 0 0 X X 0 X^2+X X 0 X^2 X 0 X 0 X^2+X X^2 X^2+X X 0 X X^2 X^2+X 0 X^2 X X^2 X X^2 0 X X^2+X X^2 X^2+X 0 0 X X X X^2 X X X^2+X X^2 X^2+X X^2+X 0 0 X^2+X X X 0 X^2+X X^2+X X X X^2 X^2 X X^2 X^2 X X^2+X 0 0 X 0 X^2 X^2+X 0 0 0 0 X^2 0 0 0 0 X^2 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 X^2 X^2 X^2 0 0 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 0 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 0 0 0 0 0 X^2 X^2 X^2 X^2 0 0 0 0 X^2 0 0 0 0 0 0 X^2 X^2 X^2 0 0 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 0 0 0 0 X^2 X^2 0 0 0 0 X^2 0 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 0 0 X^2 X^2 0 0 0 0 0 X^2 0 0 0 X^2 0 X^2 X^2 0 X^2 0 X^2 0 0 X^2 X^2 0 0 0 0 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 0 0 X^2 0 0 X^2 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 0 0 X^2 0 0 X^2 0 0 X^2 0 0 0 0 0 0 X^2 0 X^2 X^2 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 X^2 X^2 X^2 0 0 0 0 X^2 0 X^2 0 0 X^2 0 0 X^2 0 X^2 X^2 0 0 X^2 0 X^2 0 0 X^2 0 X^2 X^2 0 0 X^2 0 0 0 0 X^2 0 X^2 0 0 0 0 0 0 0 X^2 0 0 0 X^2 0 X^2 X^2 0 0 X^2 0 X^2 0 0 X^2 0 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 0 X^2 X^2 0 X^2 0 X^2 X^2 0 0 0 0 0 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 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+276x^60+182x^62+650x^64+548x^66+883x^68+596x^70+495x^72+160x^74+192x^76+38x^78+49x^80+12x^82+8x^84+5x^88+1x^100 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 12.1 seconds.