The generator matrix

 1  0  1  1  1
 0  1  1  0  0
 0  0  X  0  X
 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+53x^2+48x^3+586x^4+672x^5+586x^6+48x^7+53x^8+1x^10

The gray image is a code over GF(2) with n=20, k=11 and d=4.
This code was found by Heurico 1.16 in 0.00112 seconds.