The generator matrix

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

generates a code of length 6 over Z4 who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+39x^4+48x^6+39x^8+1x^12

The gray image is a code over GF(2) with n=12, k=7 and d=4.
This code was found by Heurico 1.16 in 0.000154 seconds.