The generator matrix

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

generates a code of length 40 over GR(16,4) who´s minimum homogenous weight is 109.

Homogenous weight enumerator: w(x)=1x^0+168x^109+312x^110+396x^111+555x^112+888x^113+672x^114+852x^115+762x^116+1224x^117+924x^118+828x^119+804x^120+1416x^121+876x^122+1068x^123+699x^124+1200x^125+828x^126+552x^127+354x^128+480x^129+228x^130+144x^131+135x^132+6x^136+9x^140+3x^148

The gray image is a code over GF(4) with n=160, k=7 and d=109.
This code was found by Heurico 1.16 in 2.13 seconds.