The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+11x^4+40x^5+10x^6+2x^8

The gray image is a code over GF(2) with n=40, k=6 and d=16.
This code was found by Heurico 1.16 in -3.24e-008 seconds.