The generator matrix

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

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+505x^76+312x^77+741x^78+304x^79+648x^80+240x^81+550x^82+240x^83+387x^84+56x^85+57x^86+20x^88+20x^90+4x^92+8x^94+1x^100+1x^104+1x^108

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 0.86 seconds.