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  X  X  X  1  1  1  1  X  X  X  1  1  1  X  X  X  1  1  1  1  X X^2 X^2 X^2  X  X  X  X  1  1  1  1 X^2 X^2 X^2  X  X  X  X  2  2  2  X  0  0  0 X^2  X X^2 X^2 X^2 X^2 X^2  2  1
 0  2  0  2  0  0  2  2  0  0  2  2  0  0  2  2  0  0  2  2  0  0  2  2  0  0  2  2  0  2  2  0  0  2  2  0  2  2  0  2  2  0  0  2  2  0  0  2  2  0  2  2  0  0  0  2  2  0  2  2  0  0  2  2  0  2  2  0  2  2  0  0  0  0  0  2  2  0  0  0
 0  0  2  2  0  2  2  0  0  2  2  0  0  2  2  0  0  2  2  0  0  2  2  0  0  2  2  0  2  2  0  0  2  2  0  2  2  0  2  2  0  0  2  2  0  0  2  2  0  2  2  0  0  0  2  2  0  2  2  0  0  2  2  0  2  2  0  0  0  2  2  0  0  0  2  2  0  0  0  0

generates a code of length 80 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+3x^80+52x^81+4x^82+4x^85

The gray image is a code over GF(2) with n=640, k=6 and d=320.
This code was found by Heurico 1.16 in 0.328 seconds.