The generator matrix

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

generates a code of length 80 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+141x^74+760x^75+1088x^76+1772x^77+1847x^78+2308x^79+1803x^80+1868x^81+1295x^82+1238x^83+781x^84+700x^85+321x^86+260x^87+104x^88+40x^89+22x^90+10x^91+13x^92+4x^93+5x^94+2x^96+1x^102

The gray image is a code over GF(2) with n=640, k=14 and d=296.
This code was found by Heurico 1.16 in 3.83 seconds.