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  1  1  X  1  1  1  1  1  X  1  1  0  1  1  1  2  1  1  X  1  1  1  1  1  1  1  0  2 2X  2  X
 0  X  0 3X+2  2 X+2 2X+2  X  0 X+2 2X X+2 3X  2  2  X  0 X+2  2 3X 2X 3X 2X 3X X+2  0 3X  2  X 2X X+2  0  2  X  0 3X+2 2X+2 3X+2 3X  0  0 X+2 3X 2X  2 3X 2X+2 3X  0  X 2X+2 3X+2  0 3X X+2  2 3X X+2 2X+2 2X+2  X 3X+2  X 3X+2 2X  0 2X  2  X X+2 X+2  2 3X+2 X+2 2X+2 2X  X  2  X 3X+2
 0  0 2X+2  0  2  0 2X  0  2  2 2X 2X+2 2X+2 2X+2  0  2  0 2X+2 2X 2X+2  2 2X  2  0  0  0 2X+2 2X+2  0  2  2 2X 2X 2X 2X+2 2X+2 2X 2X  0  0  2  2  2  2  2  2  0  0 2X+2 2X  2  0 2X 2X  0 2X  2  2  2  0 2X+2  0 2X 2X 2X+2 2X 2X  2  0 2X  2  0  2 2X+2 2X+2  2  2 2X+2  0 2X+2
 0  0  0 2X+2  0 2X 2X  2  2  2  2  0  0  2 2X+2  2 2X 2X+2 2X+2 2X  0 2X+2 2X+2 2X  0 2X+2  2 2X+2 2X+2  0 2X 2X 2X 2X+2 2X+2  2 2X+2  2 2X  0 2X 2X+2 2X 2X+2 2X 2X  2  2  2 2X 2X  2  2 2X  2  0  2  2 2X+2 2X+2  2 2X+2  0  0 2X+2 2X  0  2 2X+2 2X 2X  0  0  2 2X  0  0 2X  2  0
 0  0  0  0 2X 2X 2X 2X  0  0  0 2X  0 2X 2X 2X  0  0 2X  0  0 2X  0  0 2X  0 2X 2X  0 2X 2X 2X  0  0  0  0  0 2X 2X 2X  0 2X 2X 2X 2X  0 2X  0 2X 2X  0 2X 2X  0 2X  0  0  0  0  0 2X 2X  0  0 2X  0 2X  0 2X  0  0 2X 2X 2X 2X  0 2X  0  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+228x^74+350x^76+96x^77+596x^78+416x^79+827x^80+416x^81+564x^82+96x^83+256x^84+124x^86+92x^88+24x^90+9x^92+1x^140

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 129 seconds.