The generator matrix

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

generates a code of length 19 over Z4 who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+14x^20+1x^24

The gray image is a code over GF(2) with n=38, k=4 and d=20.
This code was found by Heurico 1.16 in 0.000753 seconds.