The generator matrix

 1  0  1  1  1  1  1  1  1  1  0  1  1  1  2  1  1  1  1  2  1  1  1  1  1  1  1  1  2 2a 2a  1  1  1  1  1  1  0
 0  1  1  a a+1  0 2a+3 a+1  2  a  1 2a+3 a+2 a+3  1  2 2a+1 a+2 a+3  1 2a+1  1  0  2  a a+2 a+1 a+3  1  1  1 2a 3a 3a+1 2a 3a 3a+1  1
 0  0 2a+2 2a  2  2  0 2a+2 2a 2a+2 2a+2  2  0 2a 2a 2a+2 2a+2  2  0  2  0  2 2a  2  0 2a 2a 2a+2 2a+2  0 2a  0 2a+2  2 2a+2  2  0  2

generates a code of length 38 over GR(16,4) who´s minimum homogenous weight is 110.

Homogenous weight enumerator: w(x)=1x^0+288x^110+180x^112+288x^114+96x^118+72x^120+96x^122+3x^128

The gray image is a code over GF(4) with n=152, k=5 and d=110.
This code was found by Heurico 1.16 in 3.25 seconds.