The generator matrix

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

generates a code of length 8 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+27x^8+4x^10

The gray image is a code over GF(2) with n=64, k=5 and d=32.
This code was found by Heurico 1.16 in 3.62e-008 seconds.