The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+48x^3+162x^4+608x^5+152x^6+48x^7+5x^8

The gray image is a code over GF(2) with n=40, k=10 and d=12.
This code was found by Heurico 1.16 in -1.01e-007 seconds.