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

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

Homogenous weight enumerator: w(x)=1x^0+288x^121+648x^122+201x^124+1008x^125+1704x^126+270x^128+1488x^129+2364x^130+174x^132+1440x^133+2124x^134+156x^136+1152x^137+1644x^138+144x^140+624x^141+732x^142+66x^144+144x^145+6x^148+3x^156+3x^160

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 2.15 seconds.