The generator matrix

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

generates a code of length 80 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+134x^76+712x^77+586x^78+816x^79+384x^80+428x^81+258x^82+264x^83+118x^84+144x^85+88x^86+88x^87+25x^88+44x^89+2x^90+2x^92+2x^94

The gray image is a code over GF(2) with n=640, k=12 and d=304.
This code was found by Heurico 1.16 in 0.391 seconds.