The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+98x^4+64x^5+88x^6+5x^8

The gray image is a code over GF(2) with n=40, k=8 and d=16.
This code was found by Heurico 1.16 in -1.01e-007 seconds.