The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+12x^10+2x^12+1x^16

The gray image is a code over GF(2) with n=20, k=4 and d=10.
This code was found by Heurico 1.16 in 0.000161 seconds.