The generator matrix
1 1 X 1 1
0 X^2+2 X^2+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+11x^4+40x^5+10x^6+2x^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 -1.01e-007 seconds.