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

generates a code of length 42 over GR(16,4) who´s minimum homogenous weight is 112.

Homogenous weight enumerator: w(x)=1x^0+72x^112+204x^116+354x^120+1317x^124+1830x^128+72x^132+93x^136+57x^140+48x^144+18x^148+15x^152+12x^156+3x^160

The gray image is a code over GF(4) with n=168, k=6 and d=112.
This code was found by Heurico 1.16 in 0.12 seconds.