The generator matrix

 1  1  X  1  1
 0 X^2+2 X^2+2  0  0
 0  0  2  0  0
 0  0  0  2  0
 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+9x^2+86x^4+320x^5+86x^6+9x^8+1x^10

The gray image is a code over GF(2) with n=40, k=9 and d=8.
This code was found by Heurico 1.16 in 0 seconds.