The generator matrix

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

generates a code of length 81 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+442x^74+1758x^75+3220x^76+4292x^77+5299x^78+6866x^79+7134x^80+7962x^81+7229x^82+6850x^83+5347x^84+4052x^85+2395x^86+1334x^87+745x^88+356x^89+133x^90+56x^91+41x^92+8x^93+6x^94+8x^96+2x^97

The gray image is a code over GF(2) with n=648, k=16 and d=296.
This code was found by Heurico 1.16 in 46.3 seconds.