The generator matrix

 1  1  1  1  1
 0  X  0  X  0
 0  0  X  X  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+84x^3+184x^4+1432x^5+184x^6+84x^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 -3.24e-008 seconds.