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 X X^2 X 0 X 0 X 0 0 X X X X X 1 1 1 1 1 0 1 0 1 1 X 1 X X 1 1 1 0 X 1 X 1 0 X 0 X 0 0 X X^2+X 0 0 X X^2+X X^2 0 X^2+X X^2 X^2+X X^2 X X X^2+X X^2 X 0 X 0 X^2 0 X X X^2+X X 0 X X^2 X^2 X X X^2+X X X^2 X^2 X^2+X X X 0 X^2 X X X 0 X 0 X X 0 0 X X X X^2+X X^2 X X^2+X X^2 X^2+X X^2 X X^2+X X^2 X^2+X X 0 0 X X 0 X^2+X X 0 0 X^2+X X 0 X X^2 X X^2 0 X^2+X X X^2+X 0 X^2+X 0 0 X X^2 X X X^2 X X^2+X X^2 X^2 X 0 0 X X 0 0 X X X^2 0 X^2 X^2+X X X X X 0 X^2 X^2 X^2+X 0 X X X^2 X^2 0 X^2 X^2 0 0 0 X X^2+X 0 X X X^2 X^2 0 0 0 X^2 0 0 0 0 0 0 0 0 0 0 X^2 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 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 X^2 0 0 X^2 0 X^2 0 X^2 0 X^2 0 0 0 0 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 X^2 0 0 0 0 0 0 X^2 0 0 0 0 0 0 0 0 X^2 0 0 0 0 0 0 0 0 0 X^2 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 X^2 X^2 0 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 0 X^2 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 0 0 0 0 X^2 0 0 0 0 0 0 X^2 0 0 0 0 X^2 X^2 X^2 X^2 0 0 0 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 0 X^2 0 0 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 0 0 0 0 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 0 0 0 0 X^2 X^2 0 0 0 0 0 0 0 X^2 0 0 0 X^2 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 0 0 0 0 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 0 X^2 0 0 0 X^2 0 X^2 0 0 X^2 0 X^2 X^2 0 0 0 0 0 0 0 X^2 0 0 X^2 X^2 X^2 X^2 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 0 X^2 0 0 0 0 X^2 0 X^2 0 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 0 0 X^2 X^2 X^2 X^2 0 0 0 0 0 0 X^2 X^2 X^2 0 0 0 0 0 0 0 0 0 0 X^2 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 0 0 0 X^2 0 X^2 X^2 0 0 0 X^2 0 X^2 X^2 0 X^2 X^2 0 0 0 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 0 0 X^2 0 0 0 0 0 0 0 0 0 0 0 0 X^2 0 X^2 0 0 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 0 X^2 0 X^2 0 0 X^2 0 0 0 X^2 0 X^2 0 X^2 0 X^2 0 X^2 0 X^2 X^2 0 0 0 0 X^2 0 X^2 X^2 0 0 0 X^2 X^2 0 0 0 X^2 X^2 X^2 0 0 X^2 0 X^2 0 X^2 X^2 generates a code of length 72 over Z2[X]/(X^3) who´s minimum homogenous weight is 60. Homogenous weight enumerator: w(x)=1x^0+180x^60+250x^62+48x^63+730x^64+152x^65+852x^66+344x^67+1371x^68+656x^69+1666x^70+848x^71+2158x^72+832x^73+1844x^74+672x^75+1375x^76+368x^77+774x^78+128x^79+595x^80+40x^81+212x^82+8x^83+182x^84+30x^86+48x^88+4x^90+11x^92+4x^96+1x^100 The gray image is a linear code over GF(2) with n=288, k=14 and d=120. This code was found by Heurico 1.16 in 25.3 seconds.