The generator matrix

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

generates a code of length 7 over Z4 who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+42x^6+7x^8+14x^10

The gray image is a code over GF(2) with n=14, k=6 and d=6.
This code was found by Heurico 1.16 in 0.000164 seconds.