The generator matrix

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

generates a code of length 4 over Z4 who´s minimum homogenous weight is 2.

Homogenous weight enumerator: w(x)=1x^0+28x^2+70x^4+28x^6+1x^8

The gray image is a code over GF(2) with n=8, k=7 and d=2.
This code was found by Heurico 1.16 in 6.01e-005 seconds.