The generator matrix

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

generates a code of length 5 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+8x^4+48x^5+4x^6+3x^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 1.05e-007 seconds.