The generator matrix

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

generates a code of length 5 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+66x^4+56x^6+5x^8

The gray image is a code over GF(2) with n=20, k=7 and d=8.
This code was found by Heurico 1.16 in 0.00025 seconds.