The generator matrix

 1  1  1  1  1
 0  2  0  2  0
 0  0  2  2  0

generates a code of length 5 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+3x^4+24x^5+3x^6+1x^10

The gray image is a code over GF(2) with n=20, k=5 and d=8.
This code was found by Heurico 1.16 in 6.29e-005 seconds.