The generator matrix

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

generates a code of length 8 over Z4[X]/(X^2+2X+2) 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 -1.01e-007 seconds.