The generator matrix

 1  1  X  X
 0  2  2  0

generates a code of length 4 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+29x^4+2x^6

The gray image is a code over GF(2) with n=32, k=5 and d=16.
This code was found by Heurico 1.16 in 6.87e-008 seconds.