The generator matrix

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

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+24x^3+194x^4+592x^5+184x^6+24x^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 3.62e-008 seconds.