The generator matrix 1 0 0 0 1 1 1 1 1 1 1 X^2 0 X^2+X X^2 0 0 1 1 0 X 1 X 0 1 1 1 X 1 X 1 1 1 1 X 1 1 0 1 1 1 X^2 0 X^2+X X X^2 X X 1 0 X^2 1 1 X^2+X 0 1 X^2+X 1 1 X^2+X 1 1 1 X^2 1 1 1 X^2 1 1 1 1 1 0 1 0 0 0 0 1 X^2+X+1 1 1 X^2+X 1 1 X 1 0 X X+1 X 1 1 X 1 X^2+X X+1 X+1 X^2+X 1 X^2+X+1 1 X^2 0 X^2+X X^2+X+1 X^2 X+1 1 1 X^2+X X^2+X X^2+1 0 1 1 1 X X^2+X X^2+X X 1 1 X+1 1 1 X X+1 1 X^2+X+1 X X^2 X+1 0 X^2 0 X^2+1 X+1 1 X^2 X^2+1 X^2+1 X^2+1 X^2+1 0 0 0 1 0 0 1 0 1 X^2+1 X^2 1 X^2+X+1 X+1 1 X^2 X 1 X^2+X+1 X+1 X^2+1 0 X^2+X X+1 1 X^2+X X^2 X+1 1 X^2+X+1 0 X X+1 1 X 1 X^2+X X^2 X^2+X+1 X^2+X 0 1 X X^2+X X+1 X X 1 1 0 X^2 1 X+1 0 X+1 1 X X^2+X X^2+X+1 X^2+X 1 0 1 1 1 X^2+1 1 X^2+1 1 X X X^2 X^2 0 0 0 0 1 1 X+1 X^2+X+1 X^2+1 X^2 X X^2+X X^2+1 0 X^2+X+1 1 1 1 X+1 X^2+X+1 X^2+X X^2+X+1 X+1 1 X^2 1 0 X^2+X 0 X^2 0 X^2+X X^2 X^2+X+1 X X X^2+1 X^2+1 X^2 0 X^2+X 0 1 X^2+1 X^2+X+1 1 1 X^2+1 X+1 X+1 0 X^2+X X^2+1 X 1 X^2+X+1 X^2 X^2+X X^2 X^2+1 X^2+X 1 X X^2+1 X 1 X+1 X^2+X+1 1 1 1 X^2+X X^2+X 0 0 0 0 0 X X X X 0 0 0 X^2+X X^2 X^2+X X^2+X X X^2+X X X^2+X X^2 X^2+X X X^2+X 0 X^2+X X^2 0 0 X^2 X X^2+X X^2+X X^2 X^2+X X 0 X^2 X X^2+X X X^2+X X 0 X^2 X^2 0 X^2+X X^2 0 0 X X^2 X 0 0 0 X^2+X X X 0 X^2 X^2+X X^2 X^2 0 0 X^2 0 X^2+X X^2+X X^2 X^2+X 0 0 0 0 0 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 0 0 0 X^2 X^2 0 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 0 0 X^2 0 0 X^2 0 0 X^2 X^2 0 0 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 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+102x^63+418x^64+660x^65+1095x^66+1314x^67+1804x^68+1920x^69+2388x^70+2454x^71+2896x^72+2618x^73+3068x^74+2370x^75+2658x^76+1970x^77+1724x^78+1114x^79+863x^80+566x^81+333x^82+210x^83+118x^84+34x^85+28x^86+18x^87+10x^88+4x^89+4x^90+2x^91+4x^93 The gray image is a linear code over GF(2) with n=292, k=15 and d=126. This code was found by Heurico 1.16 in 49.1 seconds.