The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+154x^74+672x^75+1353x^76+1448x^77+2190x^78+1820x^79+2073x^80+1712x^81+1674x^82+924x^83+1040x^84+580x^85+318x^86+192x^87+116x^88+32x^89+30x^90+36x^91+7x^92+4x^93+4x^95+2x^96+2x^98

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 3.84 seconds.