The generator matrix

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

generates a code of length 39 over GR(16,4) who´s minimum homogenous weight is 113.

Homogenous weight enumerator: w(x)=1x^0+84x^113+27x^116+48x^117+27x^120+36x^121+9x^124+24x^125

The gray image is a code over GF(4) with n=156, k=4 and d=113.
This code was found by Heurico 1.16 in 0.015 seconds.