The generator matrix

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

generates a code of length 80 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 73.

Homogenous weight enumerator: w(x)=1x^0+140x^73+782x^74+1316x^75+2259x^76+2788x^77+3562x^78+4060x^79+3959x^80+3708x^81+3425x^82+2414x^83+1734x^84+1142x^85+762x^86+340x^87+189x^88+56x^89+56x^90+26x^91+25x^92+2x^93+12x^94+4x^95+1x^96+4x^97+1x^98

The gray image is a code over GF(2) with n=640, k=15 and d=292.
This code was found by Heurico 1.16 in 13.8 seconds.