The generator matrix 1 0 1 1 1 X^2+X 1 1 0 1 1 X^2+X 1 1 X^2+X 1 1 0 1 0 1 1 1 X^2+X 1 1 0 1 1 X^2+X 1 1 1 1 X^2+X 1 1 1 X 0 1 1 0 1 1 1 1 1 X^2+X 1 X^2 0 1 X 1 1 1 1 1 1 X^2 X^2+X X 1 1 X^2+X 0 X 0 1 X+1 X^2+X 1 1 0 X+1 1 X^2+X X^2+1 1 0 X+1 1 X^2+X X^2+1 1 X^2+1 1 0 X^2+X X+1 1 X^2+X X+1 1 0 X^2 1 X^2+X X^2+1 X^2+X X^2+X+1 1 X 0 1 1 1 0 X^2+1 1 X^2+1 X+1 0 X X^2+X+1 1 X^2 1 1 X+1 1 0 X^2 X^2+X X^2+X+1 1 X^2+1 1 1 1 0 1 1 1 0 0 0 X^2 0 0 0 0 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 0 X^2 0 0 0 0 0 0 X^2 0 0 0 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 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 0 X^2 0 X^2 0 X^2 0 X^2 X^2 0 0 X^2 0 0 X^2 0 0 X^2 X^2 0 0 X^2 0 X^2 0 X^2 0 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 0 X^2 X^2 0 0 X^2 0 0 X^2 0 0 0 X^2 0 0 0 0 X^2 0 0 0 0 X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 0 0 X^2 0 0 X^2 0 X^2 0 0 0 X^2 0 0 0 0 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 0 0 0 X^2 0 X^2 X^2 X^2 X^2 0 0 0 0 0 0 0 X^2 0 0 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 0 X^2 X^2 0 0 0 X^2 X^2 X^2 0 0 0 X^2 X^2 0 0 0 X^2 X^2 0 X^2 0 X^2 X^2 0 0 X^2 0 X^2 0 X^2 X^2 0 X^2 0 0 0 0 X^2 0 0 0 X^2 0 X^2 0 0 0 0 0 0 X^2 0 X^2 0 0 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 0 0 0 0 0 0 0 X^2 X^2 X^2 0 X^2 0 0 0 0 X^2 0 X^2 0 0 0 X^2 X^2 0 0 0 0 0 0 0 0 0 X^2 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 0 0 X^2 0 X^2 X^2 0 X^2 0 0 0 0 X^2 X^2 X^2 0 0 0 X^2 0 0 X^2 X^2 0 0 X^2 0 0 X^2 0 X^2 0 X^2 X^2 0 0 0 0 0 X^2 X^2 0 X^2 X^2 X^2 0 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+126x^60+44x^61+178x^62+140x^63+386x^64+268x^65+398x^66+332x^67+424x^68+292x^69+370x^70+260x^71+377x^72+164x^73+202x^74+36x^75+58x^76+4x^78+23x^80+6x^84+5x^88+2x^92 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 1.1 seconds.