The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+39x^2+76x^3+344x^4+1128x^5+344x^6+76x^7+39x^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 -1.01e-007 seconds.