The generator matrix

 1  1  X  1  1
 0 2X  0  0 2X
 0  0 2X  0 2X
 0  0  0 2X 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+18x^4+96x^5+8x^6+5x^8

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 -1.01e-007 seconds.