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 1 0 1 X^2 1 0 X^2 0 X 1 X 1 X 0 1 1 X^2 1 1 X^2 0 1 1 1 1 1 1 X 1 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 X X^2 0 X^2 X^2 X X^2+X X^2+X X^2+X X X^2+X X^2 X X 0 X^2 X^2 X^2 0 X 0 X^2 X X 0 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^2 X 0 X^2+X 0 0 X X^2 X X^2+X X^2 X^2 X^2 0 X^2 X^2 X X^2 X^2+X X^2 X X^2 X^2 X X^2+X 0 0 X 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 0 X X^2 X X X X^2 0 0 X^2 X 0 X^2+X 0 X^2+X X^2 X^2+X 0 X^2+X X X^2 X X X^2+X X 0 X^2 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 0 X 0 X^2 0 X X^2+X X^2 X^2 X^2 X^2 X X^2 X X^2 X^2 0 X X 0 X^2 X X^2+X X 0 0 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 X^2 X^2 X^2+X X X^2+X X^2 X X^2 X X X X^2+X X X^2 X^2+X X X^2+X X^2 X^2+X X^2 0 X^2 X^2+X X^2+X X X X X^2 X^2 generates a code of length 72 over Z2[X]/(X^3) who´s minimum homogenous weight is 62. Homogenous weight enumerator: w(x)=1x^0+144x^62+4x^63+387x^64+48x^65+486x^66+156x^67+746x^68+304x^69+900x^70+496x^71+1035x^72+524x^73+816x^74+332x^75+645x^76+136x^77+408x^78+36x^79+292x^80+12x^81+154x^82+72x^84+28x^86+21x^88+8x^90+1x^108 The gray image is a linear code over GF(2) with n=288, k=13 and d=124. This code was found by Heurico 1.16 in 6.29 seconds.