The generator matrix 1 0 0 0 1 1 1 X 1 1 X X 1 1 0 1 1 1 1 2 1 X^2+X X^2+2 X^2 0 1 X^2+X+2 1 1 X^2+X 1 1 1 X^2+X X 1 X+2 X^2+2 1 X^2+X+2 1 X+2 X^2+X X^2+2 1 2 1 1 X^2+X X^2+X 1 1 X^2+X+2 1 0 1 X^2+X 1 X+2 1 1 1 1 1 1 X^2+X+2 1 1 1 X 2 1 1 X^2+X 1 0 X 1 X^2+2 X+2 1 0 1 0 0 0 X^2+3 X+3 1 1 X+1 X^2+2 1 2 X^2+X+2 1 X+3 X^2+X+1 X^2+2 0 1 X 1 X+2 1 1 X^2+2 X^2+2 X^2+1 X^2+X+1 X+2 X^2+3 X^2+1 X^2 1 1 X+2 X^2+X 1 X X X^2+X+2 1 X^2 1 X^2+3 X^2+2 X X^2+X+3 X 1 1 X+1 X X^2+X+2 X^2 X^2+2 1 0 X^2 X^2+1 X+1 X 2 X+2 0 1 X+3 3 X^2+X+1 1 X^2 2 X^2+1 1 X^2+X X^2 2 X 1 1 0 0 0 1 0 X^2 2 X^2+2 0 1 X^2+X+3 1 3 X^2+X+1 X^2+3 3 2 3 X+1 X 2 X^2+X+3 X X+2 X+1 X+1 X^2+2 1 X+1 X+2 1 X X^2+X+1 X+2 X^2+X+3 X^2+2 0 1 X X+3 1 X X^2+1 1 1 X^2+X 1 X^2+1 X+1 0 X X+1 X+3 X^2+X+2 X^2+X+2 X^2+X X^2 X^2+X+2 1 X^2 3 X^2+X X 1 X^2+X+3 X+2 X X^2+X 0 2 X^2+1 1 X^2+1 X+1 X^2+X+1 0 1 1 3 X^2+2 X^2 X^2+2 0 0 0 1 X^2+X+1 X^2+X+3 2 1 2 X+3 X^2+1 3 X^2 1 X^2+X+2 X^2+3 X+2 X^2+1 X^2+X+2 3 X^2 0 1 3 X+2 X^2+1 X 3 X^2+X+2 X+3 X^2+3 X^2+X X^2 X^2+2 X^2+X+3 X^2+3 X 2 X X^2 X+1 X+1 0 X+3 X^2 X^2+3 X^2+X+3 X+2 1 X^2+X+2 X+1 1 1 3 1 X+2 X^2+3 X^2+2 1 X^2+X+3 2 0 X^2+1 X^2+X+3 X^2+2 X^2 X^2+X+3 X^2+X+1 1 X X^2+X+3 2 2 X^2+3 X^2+X+2 X+3 X^2+X+3 1 X^2+1 X X+2 0 0 0 0 2 0 2 2 0 2 2 0 2 0 2 0 0 0 0 2 2 0 0 0 2 2 0 2 2 0 2 2 2 0 0 2 0 2 0 2 0 2 2 0 0 2 2 0 0 2 2 0 2 2 0 0 0 2 0 0 0 2 0 2 0 2 0 2 2 0 2 0 2 2 0 0 0 2 0 2 2 generates a code of length 81 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 73. Homogenous weight enumerator: w(x)=1x^0+314x^73+1442x^74+3538x^75+5289x^76+8096x^77+10795x^78+13434x^79+14401x^80+16712x^81+14735x^82+13776x^83+10602x^84+7716x^85+4691x^86+2870x^87+1420x^88+736x^89+311x^90+98x^91+43x^92+24x^93+10x^94+12x^95+2x^96+2x^97+2x^100 The gray image is a code over GF(2) with n=648, k=17 and d=292. This code was found by Heurico 1.16 in 188 seconds.