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  0 2X  1  1 2X  1  1 2X  1 X+2  1  1 3X+2  1 3X  0 2X+2 2X+2  1 X+2  1  2  X  1  1  2  1  0  1 3X 2X+2  1 X+2  1  1 3X+2  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 2X+2  1  1  1 X+2  1 3X+1  1 3X+2  1  0 X+2  1  1 X+1  1 X+2 3X+2  1  2  1 3X 2X+1  1 2X+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 2X+2 3X+1 X+1 2X  0 3X+2 3X+3  1 3X+1 X+1 3X+3  1  X  2  0 X+3  1 3X+2 2X+2 3X+2  X 2X+3  1 2X+3 2X+3  1  X  3  2 2X+2  X 3X+1 3X 2X X+1 3X+1  0
 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  3 2X X+1 3X+1 X+3 2X+3  1  3  X 3X+3 X+2 X+2  1  1  2 X+1 X+2 X+1 3X+3 3X+2  2 3X+3  X  2 2X  1 X+2  2 2X+3  1 2X+1 X+2  0 X+3 X+3  0 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+360x^73+1832x^74+2852x^75+4470x^76+5500x^77+6911x^78+6982x^79+8280x^80+7184x^81+6912x^82+5116x^83+4140x^84+2292x^85+1455x^86+634x^87+366x^88+118x^89+42x^90+48x^91+10x^92+16x^93+8x^94+5x^96+2x^97

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 46.5 seconds.