The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+62x^4+1x^8

The gray image is a code over GF(2) with n=32, k=6 and d=16.
This code was found by Heurico 1.16 in 3.81e-009 seconds.