The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+9x^4+18x^5+13x^6+12x^7+6x^8+2x^9+3x^10

The gray image is a code over GF(2) with n=12, k=6 and d=4.
This code was found by Heurico 1.16 in 8.92e-005 seconds.