The generator matrix

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

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+15x^4+96x^5+15x^6+1x^10

The gray image is a code over GF(2) with n=40, k=7 and d=16.
This code was found by Heurico 1.16 in 0 seconds.