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 0 X X^2 0 0 1 X^2 1 X 1 X^2 1 X 1 X 1 1 0 1 X X 1 X 1 1 X 0 X^2 0 X^2 X 1 1 1 1 0 X X 1 0 X 0 0 0 0 0 0 0 X^2+X X X X X X^2 X^2+X 0 X X X^2+X X^2 X^2+X X X^2 X X 0 0 X^2+X X^2 0 X^2 X X^2+X X 0 0 0 X^2 X^2 X X^2 X^2 0 X^2 X^2+X X X^2+X X X X^2+X X 0 0 X X^2 X^2+X X X 0 X^2 X^2+X X^2 X X 0 X^2+X 0 X 0 0 X X X 0 0 0 X 0 0 0 X X^2+X X X^2 X X^2+X 0 0 X X X^2 X^2+X X X^2 X X X X X^2 X^2 0 X^2+X X 0 0 X^2+X X X^2+X X X^2 X^2 X^2+X 0 X X X X 0 0 X 0 X^2 X X^2 0 X^2+X 0 X 0 X X^2+X 0 X^2+X 0 X^2 X^2 X 0 X^2 X X X^2 X X^2+X X^2+X 0 X^2+X X^2+X 0 0 0 0 X 0 X X X 0 X^2+X X^2 X X^2+X 0 X 0 X X X^2+X 0 0 X^2 X X X^2+X X^2 0 X^2+X X^2 X^2+X X^2 X 0 0 X X^2 X X X X^2 X 0 X X^2 X^2 X^2+X X X X X^2+X 0 X^2 0 0 X X^2+X X X^2+X X^2+X 0 X^2+X X X X 0 X^2+X X X X^2+X 0 X^2+X X^2+X X X 0 0 0 0 0 X X 0 X X^2+X X 0 X X^2 X^2+X X^2+X X 0 X 0 0 X^2 X^2 0 X^2+X X X^2+X X^2 0 X^2+X 0 X^2+X X^2 0 X^2+X X^2+X X X^2 X X X^2 X^2 X^2 0 0 X^2+X 0 X^2+X 0 X X 0 X^2+X X^2 X^2 0 X^2 X^2+X X^2 X 0 X 0 X 0 X^2+X X X^2+X X X^2 X^2 X^2+X X 0 X 0 0 0 0 0 0 X^2 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 0 X^2 0 X^2 X^2 0 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 0 0 X^2 0 0 0 X^2 0 0 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 0 0 X^2 X^2 X^2 0 0 0 0 0 0 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 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 X^2 0 X^2 0 X^2 0 0 0 X^2 X^2 0 0 0 0 0 0 0 X^2 X^2 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 generates a code of length 75 over Z2[X]/(X^3) who´s minimum homogenous weight is 64. Homogenous weight enumerator: w(x)=1x^0+33x^64+96x^65+163x^66+214x^67+281x^68+326x^69+370x^70+474x^71+574x^72+646x^73+663x^74+730x^75+661x^76+550x^77+580x^78+462x^79+334x^80+256x^81+181x^82+180x^83+129x^84+78x^85+66x^86+48x^87+25x^88+26x^89+25x^90+4x^91+9x^92+6x^93+1x^104 The gray image is a linear code over GF(2) with n=300, k=13 and d=128. This code was found by Heurico 1.16 in 6.64 seconds.