The generator matrix

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

generates a code of length 80 over Z4[X]/(X^3+2,2X) 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.