The generator matrix

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

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+16x^3+66x^4+96x^5+56x^6+16x^7+5x^8

The gray image is a code over GF(2) with n=20, k=8 and d=6.
This code was found by Heurico 1.16 in 0.00011 seconds.