The generator matrix

 1  0  1  1  1
 0  1  1 2X+2 3X+1
 0  0  X X+2  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+64x^3+354x^4+1216x^5+344x^6+64x^7+5x^8

The gray image is a code over GF(2) with n=40, k=11 and d=12.
This code was found by Heurico 1.16 in -1.01e-007 seconds.