The generator matrix

 1  0  0  1  1
 0  1  0  1  2
 0  0  1  1  0
 0  0  0  X X^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+117x^2+912x^3+5514x^4+19680x^5+5514x^6+912x^7+117x^8+1x^10

The gray image is a code over GF(2) with n=40, k=15 and d=8.
This code was found by Heurico 1.16 in 0.141 seconds.