The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  X  1  1 2X+2  1  X  1  X  X  1  X  1  X 2X+2  2  0 2X+2  X  1  X 2X  X  X  1  1  1
 0  X  0  X 2X  0 X+2 3X+2  0 2X 3X 3X  0 2X 3X+2 3X+2 3X+2 2X+2 3X+2 2X+2 2X+2  X  X  2 2X+2  X X+2  2 2X+2  X 2X+2 3X X+2  0 3X+2  2 3X 3X 3X  0  2  X  X  X 2X+2 3X+2 2X+2  0 X+2  X  X  0 2X  2  X 3X+2 3X+2  X 2X+2 3X 2X  0 2X 2X 3X+2 2X  X  X  X  X  X 3X 2X+2 3X+2  X X+2 X+2 3X+2 3X  0
 0  0  X  X  0 3X+2 X+2 2X  2 3X+2 3X+2  2 2X+2 3X  X  2  0  X 3X+2 2X 2X X+2  0  X  2 3X 2X X+2 2X+2  X X+2  2 3X 2X  2  0  0  2 3X  X X+2 3X+2  0 3X+2 2X+2 X+2 3X 2X+2 3X 2X+2 2X+2  0 X+2 X+2 2X 2X+2  2 X+2 3X 3X  2 3X+2  X  0 X+2 2X+2  2 X+2  0 X+2 2X  2  0 3X  2 2X 3X  X 2X+2  0
 0  0  0  2 2X+2  2 2X  2  2  0  2 2X+2  0  2 2X  0 2X 2X+2  2  0  2 2X 2X+2  0  2 2X+2 2X+2 2X  0  0  2  0  2 2X 2X 2X+2  2  2 2X 2X 2X+2  0 2X 2X+2 2X  0 2X 2X+2 2X+2  0 2X  2 2X+2  0 2X+2 2X+2  2  0  2  2 2X  2  0  2  0  2  2  2  0 2X  2 2X+2  0 2X 2X+2  0  2 2X+2 2X+2  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+78x^74+216x^75+265x^76+360x^77+444x^78+586x^79+515x^80+354x^81+472x^82+256x^83+146x^84+188x^85+70x^86+58x^87+32x^88+26x^89+22x^90+4x^91+1x^92+1x^94+1x^126

The gray image is a code over GF(2) with n=640, k=12 and d=296.
This code was found by Heurico 1.16 in 0.875 seconds.