The generator matrix

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

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+390x^73+1852x^74+2616x^75+4546x^76+5378x^77+7120x^78+7426x^79+8155x^80+6890x^81+7036x^82+4978x^83+4102x^84+2130x^85+1537x^86+694x^87+404x^88+184x^89+48x^90+30x^91+8x^92+4x^93+6x^94+1x^102

The gray image is a code over GF(2) with n=640, k=16 and d=292.
This code was found by Heurico 1.16 in 43.8 seconds.