The generator matrix

 1  1  1  1  X
 0 X^2+2  0  0 X^2+2
 0  0 X^2+2  0 X^2
 0  0  0 X^2+2 X^2
 0  0  0  0  2

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

Homogenous weight enumerator: w(x)=1x^0+45x^2+338x^4+1280x^5+338x^6+45x^8+1x^10

The gray image is a code over GF(2) with n=40, k=11 and d=8.
This code was found by Heurico 1.16 in 1.05e-007 seconds.