The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+100x^73+765x^74+1568x^75+2128x^76+2800x^77+3386x^78+4148x^79+3708x^80+4076x^81+3140x^82+2618x^83+1839x^84+1136x^85+602x^86+348x^87+204x^88+66x^89+68x^90+18x^91+23x^92+12x^93+6x^94+4x^95+1x^96+2x^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 13.5 seconds.