The generator matrix

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

generates a code of length 5 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 3.

Homogenous weight enumerator: w(x)=1x^0+48x^3+162x^4+608x^5+152x^6+48x^7+5x^8

The gray image is a code over GF(2) with n=40, k=10 and d=12.
This code was found by Heurico 1.16 in -3.24e-008 seconds.