The generator matrix

 1  0  1 3X+2  X
 0  1 3X+2  1 3X+2
 0  0 2X 2X  0

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

Homogenous weight enumerator: w(x)=1x^0+162x^4+192x^5+152x^6+5x^8

The gray image is a code over GF(2) with n=40, k=9 and d=16.
This code was found by Heurico 1.16 in 3.81e-009 seconds.