The generator matrix

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

generates a code of length 44 over GR(16,4) who´s minimum homogenous weight is 121.

Homogenous weight enumerator: w(x)=1x^0+300x^121+384x^122+264x^123+270x^124+1284x^125+1080x^126+528x^127+438x^128+1524x^129+1116x^130+564x^131+375x^132+1560x^133+1452x^134+420x^135+465x^136+1380x^137+948x^138+372x^139+207x^140+708x^141+396x^142+156x^143+21x^144+156x^145+9x^148+3x^152+3x^156

The gray image is a code over GF(4) with n=176, k=7 and d=121.
This code was found by Heurico 1.16 in 16.7 seconds.