The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+39x^2+84x^3+184x^4+408x^5+184x^6+84x^7+39x^8+1x^10

The gray image is a code over GF(2) with n=20, k=10 and d=4.
This code was found by Heurico 1.11 in 8.51e-005 seconds.