The generator matrix

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

generates a code of length 38 over GR(16,4) who´s minimum homogenous weight is 113.

Homogenous weight enumerator: w(x)=1x^0+72x^113+144x^114+24x^117+9x^120+6x^124

The gray image is a code over GF(4) with n=152, k=4 and d=113.
This code was found by Heurico 1.16 in 0.015 seconds.