The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+210x^112+360x^113+84x^114+588x^115+1098x^116+1104x^117+180x^118+888x^119+1587x^120+1224x^121+204x^122+936x^123+1326x^124+1320x^125+108x^126+864x^127+1614x^128+912x^129+144x^130+492x^131+492x^132+456x^133+48x^134+72x^135+57x^136+6x^140+3x^144+6x^148

The gray image is a code over GF(4) with n=164, k=7 and d=112.
This code was found by Heurico 1.16 in 0.562 seconds.