The generator matrix

 1  0  1  1  1
 0  1 X+1  0  0
 0  0  2  0  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+15x^2+64x^4+96x^5+64x^6+15x^8+1x^10

The gray image is a code over GF(2) with n=20, k=8 and d=4.
This code was found by Heurico 1.16 in 7.3e-005 seconds.