The generator matrix

 1  1  1  1  X
 0  X  0 X+2  2
 0  0  2  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+18x^4+32x^5+8x^6+5x^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 0.000104 seconds.