The generator matrix

 1  0  0  0  1  1
 0  1  0  0  2  1
 0  0  1  0  3  1
 0  0  0  1  1  2

generates a code of length 6 over Z4 who´s minimum homogenous weight is 3.

Homogenous weight enumerator: w(x)=1x^0+16x^3+39x^4+48x^5+48x^6+48x^7+39x^8+16x^9+1x^12

The gray image is a code over GF(2) with n=12, k=8 and d=3.
This code was found by Heurico 1.16 in 0.000227 seconds.