The generator matrix

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

generates a code of length 44 over GR(16,4) who´s minimum homogenous weight is 124.

Homogenous weight enumerator: w(x)=1x^0+105x^124+288x^125+324x^126+72x^127+423x^128+804x^129+24x^130+36x^131+303x^132+456x^133+24x^134+60x^135+165x^136+324x^137+24x^138+12x^139+156x^140+192x^141+180x^142+12x^143+63x^144+48x^145

The gray image is a code over GF(4) with n=176, k=6 and d=124.
This code was found by Heurico 1.16 in 0.063 seconds.