The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+15x^2+96x^4+288x^5+96x^6+15x^8+1x^10

The gray image is a code over GF(2) with n=40, k=9 and d=8.
This code was found by Heurico 1.16 in -6.48e-008 seconds.