The generator matrix

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

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+41x^2+72x^3+598x^4+2672x^5+598x^6+72x^7+41x^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 0.015 seconds.