The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+1110x^112+4770x^116+9711x^120+14895x^124+18867x^128+12435x^132+3516x^136+123x^140+66x^144+27x^148+9x^152+6x^156

The gray image is a code over GF(4) with n=168, k=8 and d=112.
This code was found by Heurico 1.16 in 28.7 seconds.