The generator matrix

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

generates a code of length 80 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+320x^72+1660x^73+3154x^74+5330x^75+8003x^76+10760x^77+12938x^78+15384x^79+16368x^80+15328x^81+12965x^82+10740x^83+7970x^84+5248x^85+2582x^86+1204x^87+591x^88+324x^89+98x^90+60x^91+25x^92+8x^93+6x^94+2x^96+2x^99+1x^106

The gray image is a code over GF(2) with n=640, k=17 and d=288.
This code was found by Heurico 1.16 in 173 seconds.