The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+16x^3+98x^4+288x^5+88x^6+16x^7+5x^8

The gray image is a code over GF(2) with n=40, k=9 and d=12.
This code was found by Heurico 1.16 in 1.05e-007 seconds.