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^2 X X X^2 1 0 X 1 X^2 X 1 X^2 1 X 1 X 1 0 1 1 X 0 1 0 0 0 1 1 0 1 1 X X X 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 X X^2 X X^2+X X^2 X X X^2 X X X X^2+X X X X^2+X 0 X 0 X 0 X^2+X X X X X 0 X^2 X 0 X X^2 X X^2+X 0 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^2 X^2 0 X X 0 X 0 0 X 0 X^2 X^2 X^2 X 0 0 X X^2+X 0 X^2 X X X 0 X^2 X X 0 X^2+X X^2 X^2+X X^2+X X^2 0 0 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 X^2+X X X^2+X X^2+X X 0 X 0 X 0 X^2+X X X 0 X^2+X X X^2 X X X^2 X X^2+X 0 X^2 X^2+X X X^2 X^2 X^2 0 X^2+X X^2 0 X^2 X 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^2+X 0 X X 0 X^2+X X X X^2 X 0 0 X X 0 0 X^2 0 X 0 X X^2 X X^2+X X^2 X^2 X X^2+X 0 X^2 X^2+X 0 X^2+X 0 X 0 0 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 0 X^2 0 X X^2 0 X^2+X X X 0 X^2 X X X^2 0 0 X^2 X 0 X X^2+X X^2+X 0 0 X X^2+X X X 0 X^2 0 0 0 X^2 0 X^2 0 generates a code of length 75 over Z2[X]/(X^3) who�s minimum homogenous weight is 65. Homogenous weight enumerator: w(x)=1x^0+82x^65+186x^66+214x^67+286x^68+330x^69+429x^70+470x^71+559x^72+694x^73+632x^74+716x^75+625x^76+574x^77+558x^78+372x^79+382x^80+308x^81+188x^82+154x^83+121x^84+104x^85+70x^86+46x^87+42x^88+20x^89+14x^90+12x^91+2x^94+1x^102 The gray image is a linear code over GF(2) with n=300, k=13 and d=130. This code was found by Heurico 1.16 in 58.8 seconds.