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

generates a code of length 41 over GR(16,4) who´s minimum homogenous weight is 112.

Homogenous weight enumerator: w(x)=1x^0+321x^112+48x^114+432x^118+297x^120+1296x^122+1296x^126+189x^128+126x^136+81x^144+9x^152

The gray image is a code over GF(4) with n=164, k=6 and d=112.
This code was found by Heurico 1.16 in 3.63 seconds.