The generator matrix

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

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+19x^4+24x^5+18x^6+2x^8

The gray image is a code over GF(2) with n=20, k=6 and d=8.
This code was found by Heurico 1.16 in 4.82e-005 seconds.