The generator matrix

 1  0  0  1  1
 0  1  0  X  3
 0  0  1  1 X+1

generates a code of length 5 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 3.

Homogenous weight enumerator: w(x)=1x^0+48x^3+98x^4+224x^5+88x^6+48x^7+5x^8

The gray image is a code over GF(2) with n=20, k=9 and d=6.
This code was found by Heurico 1.13 in -9.54e-008 seconds.