The generator matrix

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

generates a code of length 10 over Z4 who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+13x^8+24x^9+8x^10+2x^12+8x^13+8x^14

The gray image is a code over GF(2) with n=20, k=6 and d=8.
This code was found by Heurico 1.16 in 0.000272 seconds.