The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+231x^112+288x^113+732x^114+1056x^115+1752x^116+1368x^117+1812x^118+2352x^119+2577x^120+2484x^121+2940x^122+3492x^123+4458x^124+3336x^125+3804x^126+4656x^127+5412x^128+3552x^129+3672x^130+3672x^131+4011x^132+2400x^133+2112x^134+1536x^135+975x^136+396x^137+288x^138+132x^139+24x^140+12x^144+3x^148

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 10.6 seconds.