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 0 1 1 1 X 0 1 1 X 1 0 1 0 1 0 X 1 0 1 1 1 X X X X X 1 X X 1 X^2 0 X X 0 0 X 0 0 0 0 0 0 X^2 X X^2+X X^2+X X X X^2+X X^2+X X^2 X^2 0 X X X^2+X X 0 X X 0 X^2+X X X^2 X^2 X^2 X^2+X X^2+X 0 X^2+X X^2+X X X^2 X^2+X X^2+X X^2+X X X^2+X X X^2+X X X X^2 0 X X 0 X X X^2+X X X X^2 X X^2+X X^2+X X 0 X^2+X X X X X X^2+X X^2+X X^2 0 0 X 0 0 0 X X^2+X X^2+X X X X^2 X X X^2 0 X^2 X^2+X X^2+X X^2+X 0 X X^2+X X^2+X 0 X^2+X X^2+X X^2 X^2 0 0 X^2 X^2 X^2+X 0 X^2+X X^2+X X^2+X X^2 X^2 X^2+X 0 0 X X^2+X 0 X^2+X X^2 X^2 X^2 0 X^2 X X X 0 X^2 X^2+X X^2 X^2+X X^2 X^2 X X^2+X X^2+X X 0 X^2 0 X^2+X X^2 0 0 0 0 X 0 X X X 0 X^2 0 X X^2+X X^2+X X X^2 X^2 0 0 0 X^2 X^2 X^2+X X X^2+X X X 0 X X^2 X^2+X X^2+X X^2+X X X^2+X X^2+X X^2+X X X 0 X^2 X^2 0 X^2 X^2+X X X^2+X 0 X^2+X X^2 X X^2+X 0 0 X 0 X^2 X X X^2 X 0 X X^2+X X^2+X 0 X X X^2+X 0 X^2 X 0 0 0 0 X X X^2 X^2+X X X^2 X 0 X 0 X X X^2+X X^2+X 0 X^2 X X X^2 0 X^2 X^2+X X^2+X 0 X 0 X^2 X X^2+X X X^2+X X^2 X^2+X X^2 0 0 X X^2 X^2 0 X^2+X X^2+X X^2 X^2 X^2 X 0 X 0 X^2+X 0 0 0 X^2 X X^2 0 X^2+X X X^2+X X X^2 X^2+X X^2 0 X^2+X X^2+X X^2 0 0 0 0 0 X^2 X^2 X^2 0 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 0 0 0 X^2 0 X^2 0 0 X^2 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 0 X^2 0 0 0 X^2 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 generates a code of length 72 over Z2[X]/(X^3) who´s minimum homogenous weight is 64. Homogenous weight enumerator: w(x)=1x^0+207x^64+24x^65+342x^66+108x^67+389x^68+152x^69+486x^70+244x^71+435x^72+188x^73+376x^74+200x^75+335x^76+80x^77+192x^78+20x^79+144x^80+4x^81+84x^82+4x^83+51x^84+22x^86+4x^88+2x^90+1x^96+1x^100 The gray image is a linear code over GF(2) with n=288, k=12 and d=128. This code was found by Heurico 1.16 in 97.1 seconds.