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 1 1 X^2 X X X X^2 0 0 X X X^2 1 1 1 X 1 X^2 0 X^2 X^2 1 X^2 1 X 1 1 0 0 1 X^2 X^2 1 X X 1 X 0 X 0 0 0 0 0 0 X^2 X^2 X X^2+X X 0 0 X^2 X^2+X X^2+X X X X X 0 X X^2+X X 0 X X^2+X X^2 X^2+X X^2 X^2 X^2+X X 0 0 X X^2 X^2 X^2+X X^2 X X X^2 X X^2+X X X^2+X 0 0 X 0 X^2 0 X^2 X^2 X^2 X X X X X^2 0 0 X^2+X 0 0 X^2 0 X^2+X X^2+X X 0 0 X 0 0 0 0 0 0 0 0 0 X^2 X^2+X X^2+X X^2+X X X^2+X X^2+X X X^2 X^2 X^2+X X^2+X 0 0 X X X X^2+X X^2+X X^2+X X^2 X^2 X^2+X X X X^2 X^2 X X 0 X X X X^2 X X^2+X X X^2+X X^2+X 0 X X 0 X^2 X X^2 X X^2 X 0 0 X X 0 X X X 0 0 X^2 X^2+X 0 0 0 X 0 0 X^2 X^2+X X X X X X^2 X^2+X X X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X X^2+X X X^2 X X^2+X X^2+X X X^2+X 0 X^2 0 0 0 X^2+X X^2 X X^2+X 0 0 0 X X^2+X X^2+X X X 0 X^2+X X^2+X X^2+X X X 0 0 X^2+X X^2+X X^2+X X^2+X X^2 X^2+X 0 X X X^2+X X^2 X^2 X 0 0 X^2+X 0 0 0 0 X 0 X^2+X X^2+X X X^2 X^2+X X^2+X 0 X X 0 X^2 X 0 X^2+X X^2+X X X^2+X X X^2 X^2 X X^2 X^2 0 X^2+X X^2 0 X^2+X X X^2+X X^2 0 X 0 0 X^2 0 X^2+X X 0 0 X^2+X X^2+X X^2 X X X^2 X^2+X X^2 X 0 X^2+X X X^2 X X^2+X 0 X X X^2 X X^2+X X X^2+X X^2+X X^2 X 0 0 0 0 0 X X X^2 X^2+X X X^2+X X^2 X X 0 X 0 X^2+X X^2+X 0 X X^2 X^2 X^2+X X^2 X X^2+X X^2+X X^2 X X^2 X^2 X^2+X 0 X X^2+X 0 0 X X 0 X^2+X X^2 0 0 X^2 X^2 0 X^2 X 0 X X 0 0 0 X^2+X X X^2+X X^2 0 X^2+X 0 X^2 X X^2+X X^2+X X^2 X^2+X X 0 X X^2 generates a code of length 73 over Z2[X]/(X^3) who´s minimum homogenous weight is 63. Homogenous weight enumerator: w(x)=1x^0+98x^63+170x^64+172x^65+275x^66+338x^67+457x^68+526x^69+548x^70+688x^71+627x^72+608x^73+654x^74+656x^75+570x^76+404x^77+328x^78+270x^79+209x^80+152x^81+156x^82+98x^83+69x^84+54x^85+20x^86+24x^87+9x^88+4x^89+2x^90+4x^91+1x^98 The gray image is a linear code over GF(2) with n=292, k=13 and d=126. This code was found by Heurico 1.16 in 20.4 seconds.