The generator matrix

 1  0  0  1  1
 0  1  0  1  0
 0  0  1  1  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+87x^2+420x^3+1096x^4+4984x^5+1096x^6+420x^7+87x^8+1x^10

The gray image is a code over GF(2) with n=40, k=13 and d=8.
This code was found by Heurico 1.16 in -8.01e-008 seconds.