The generator matrix

 1  1  1  1  1
 0  2  0  2  0
 0  0  2  2  0

generates a code of length 5 over Z4 who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+3x^4+8x^5+3x^6+1x^10

The gray image is a code over GF(2) with n=10, k=4 and d=4.
This code was found by Heurico 1.16 in 5.29e-005 seconds.