The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+6x^4+8x^5+4x^6+8x^7+1x^8+4x^10

The gray image is a code over GF(2) with n=12, k=5 and d=4.
This code was found by Heurico 1.16 in 7.3e-005 seconds.