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.