The generator matrix

 1  1  X  X  1
 0  X  X  0  0
 0  0 X^2 X^2+2  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+25x^2+72x^3+358x^4+1136x^5+358x^6+72x^7+25x^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 0.016 seconds.