The generator matrix

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

generates a code of length 44 over GR(16,4) who´s minimum homogenous weight is 115.

Homogenous weight enumerator: w(x)=1x^0+504x^115+945x^116+684x^117+1488x^118+2628x^119+3297x^120+1800x^121+4128x^122+7236x^123+7998x^124+3528x^125+8556x^126+15264x^127+14721x^128+6240x^129+14652x^130+24240x^131+20151x^132+8556x^133+17016x^134+25380x^135+19167x^136+6552x^137+12168x^138+13572x^139+9639x^140+2880x^141+3084x^142+3192x^143+1770x^144+480x^145+348x^146+144x^147+69x^148+30x^152+21x^156+6x^160+9x^164

The gray image is a code over GF(4) with n=176, k=9 and d=115.
This code was found by Heurico 1.16 in 275 seconds.