The generator matrix

 1  0  1  X  1
 0  1  1  2  0
 0  0  X  X  0
 0  0  0 2X  0

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

Homogenous weight enumerator: w(x)=1x^0+55x^2+212x^3+680x^4+2200x^5+680x^6+212x^7+55x^8+1x^10

The gray image is a code over GF(2) with n=40, k=12 and d=8.
This code was found by Heurico 1.16 in 3.81e-009 seconds.