The generator matrix

 1  0  0  0  1  1  1 2X+2  1  1 2X  1  1  0 3X+2  1  X 3X 2X+2  1  1 2X+2  1  1  X  2  1  2  1  1  2  1 3X+2  1  1  1 2X  1 2X+2  0  0 3X+2 X+2  1  1  1  1  1  1 3X+2  1  2  1  1 3X 2X 3X+2  1  1 3X X+2 2X+2  1 X+2  1  2  1 2X  1  X  2  1  1  0  1 3X  1  1  1  1  1
 0  1  0  0  X 2X+3 X+3  1 3X+2 X+1  1 2X 2X+1 3X  1 X+1 2X  1  1 2X+2  3 3X 3X+2  0  1 2X+2 2X+1  1  0 3X+1 3X+2 X+2  1 2X+1 X+3 3X+1  1 3X+3  0  1  1  1  1 3X+2 3X+2  1  2 2X+1 2X+1  1 2X+3  1  3 3X+2 3X+2  1  1 3X 2X  2 3X+2  2 2X  0  X  2 3X+3 X+2 X+3  1  X 3X  3 3X  2  1  2 3X+2 3X+3 X+2 2X+2
 0  0  1  0  0 2X+2 2X  1 2X+1  1 X+1 2X+1 2X+3  1  0 X+3  1  2  3 3X 3X+2  X 3X+3 2X+1 X+1  1 3X  0 2X+2 3X+3  0 3X 2X+3 2X 3X  3  X  1  1 3X+1 3X+2 X+3 X+1  2  1 X+2 2X+3 2X+3 X+2 X+2  2  0 3X+1 3X+3  1  X 3X+2 3X+1 2X+3  1  1  1  1 2X 3X 2X  2  1 X+3 3X+3  1 2X+1 3X  2 3X 2X  0 3X 3X 2X+3 2X
 0  0  0  1  1 3X+3 3X X+1 X+2 2X+3 3X+2 X+1  0  1 3X+3  3 X+1  X  X X+3  X  1 X+3 3X X+1 X+2 3X+3 2X+3  X 2X  1 2X+3 3X+1 2X+1  X 3X X+1  3 3X+1 3X 2X+2 X+3  2  2 X+3  1  1  1 2X 2X+3 2X+2 2X  2  1 3X+2 2X+1 X+2 X+2 X+2  2 3X+3 2X+2 3X+3  1 X+2  1  2 X+1 X+1 2X+2 2X+2 2X+1  X  1 2X+3  3 X+1  1  1  3 3X
 0  0  0  0 2X+2  0 2X+2  0 2X+2 2X+2  2  0  0 2X+2 2X+2  2 2X+2  0 2X+2 2X+2  2  0 2X  2 2X  0  0 2X+2 2X  0 2X 2X+2 2X  0 2X  2 2X  0 2X  0 2X+2  2 2X  0  2 2X+2 2X  2 2X 2X+2 2X  2  0  2 2X  0  0 2X+2  0  2  2 2X+2  2 2X  0 2X+2 2X+2 2X  2  2 2X  0 2X+2  2  0  2 2X  0 2X  2  0

generates a code of length 81 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+269x^72+1414x^73+3350x^74+6166x^75+10211x^76+14730x^77+21110x^78+26284x^79+31266x^80+31736x^81+31513x^82+27394x^83+21689x^84+15006x^85+9556x^86+5158x^87+2967x^88+1328x^89+525x^90+252x^91+121x^92+52x^93+24x^94+6x^95+3x^96+4x^97+2x^98+4x^99+2x^105+1x^108

The gray image is a code over GF(2) with n=648, k=18 and d=288.
This code was found by Heurico 1.16 in 767 seconds.