The generator matrix

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

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+93x^2+288x^3+1058x^4+1216x^5+1058x^6+288x^7+93x^8+1x^10

The gray image is a code over GF(2) with n=20, k=12 and d=4.
This code was found by Heurico 1.16 in 0.00343 seconds.