The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+25x^74+224x^75+303x^76+384x^77+402x^78+516x^79+507x^80+436x^81+398x^82+424x^83+193x^84+136x^85+66x^86+52x^87+19x^88+4x^89+3x^90+2x^106+1x^128

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 0.594 seconds.