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 X 1 1 1 1 X 1 X 0 1 1 1 1 X 1 0 1 1 X 1 0 0 1 1 X X^2 1 X 0 1 1 X^2 1 X 0 X 0 X 0 0 X X^2+X 0 X^2 X^2+X X 0 X X 0 X^2 X X^2+X X^2 0 X^2 X X^2 X 0 X^2 X X^2+X 0 X^2+X X^2+X X^2 X^2 X^2 X X^2+X X 0 X^2 0 X^2+X X^2+X X^2 X^2 0 X^2+X 0 X X^2+X X X^2+X X^2 X X^2 0 0 0 0 X X 0 X 0 X^2 X^2+X X 0 0 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 X X^2 X^2 X^2 X 0 X^2 X^2+X 0 X^2+X 0 0 X^2+X X X X^2 0 X X 0 X X^2 X X^2+X X 0 X 0 0 X^2 0 X X X^2 X X^2+X X^2+X X^2 X X X^2+X X 0 X^2 X X^2+X X X X 0 0 X^2+X 0 0 0 X^2 0 0 0 0 X^2 X^2 X^2 0 X^2 0 X^2 0 0 X^2 X^2 0 X^2 0 0 0 X^2 X^2 0 0 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 0 0 0 X^2 0 0 0 X^2 X^2 0 X^2 0 0 X^2 0 X^2 0 0 X^2 0 X^2 X^2 0 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 0 0 X^2 0 0 0 0 0 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 0 X^2 0 0 0 0 0 0 0 X^2 X^2 0 0 0 0 0 0 X^2 0 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 0 0 X^2 X^2 0 0 X^2 X^2 0 X^2 0 X^2 X^2 0 0 0 0 X^2 X^2 0 X^2 0 0 X^2 0 X^2 X^2 X^2 0 X^2 0 0 0 0 0 0 0 X^2 X^2 X^2 0 0 X^2 0 0 X^2 X^2 0 0 0 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 0 X^2 0 0 0 0 X^2 0 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 0 0 0 X^2 0 0 X^2 X^2 0 0 0 0 X^2 X^2 X^2 0 0 0 X^2 X^2 0 X^2 0 0 0 0 0 0 0 X^2 0 0 0 X^2 0 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 0 0 0 X^2 X^2 0 X^2 X^2 0 0 0 X^2 X^2 0 X^2 0 0 X^2 0 X^2 X^2 0 X^2 0 0 0 X^2 X^2 0 X^2 X^2 0 0 0 X^2 0 X^2 X^2 0 0 generates a code of length 69 over Z2[X]/(X^3) who´s minimum homogenous weight is 60. Homogenous weight enumerator: w(x)=1x^0+127x^60+206x^62+28x^63+333x^64+96x^65+396x^66+232x^67+535x^68+320x^69+462x^70+224x^71+433x^72+96x^73+242x^74+24x^75+150x^76+92x^78+4x^79+62x^80+10x^82+19x^84+3x^88+1x^108 The gray image is a linear code over GF(2) with n=276, k=12 and d=120. This code was found by Heurico 1.16 in 1.52 seconds.