The generator matrix

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

generates a code of length 40 over GR(16,4) who´s minimum homogenous weight is 113.

Homogenous weight enumerator: w(x)=1x^0+348x^113+324x^114+336x^115+171x^116+324x^117+420x^118+252x^119+150x^120+276x^121+312x^122+216x^123+57x^124+108x^125+180x^126+108x^127+66x^128+288x^129+108x^130+48x^131+3x^136

The gray image is a code over GF(4) with n=160, k=6 and d=113.
This code was found by Heurico 1.16 in 0.031 seconds.