The generator matrix

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

generates a code of length 44 over GR(16,4) who´s minimum homogenous weight is 125.

Homogenous weight enumerator: w(x)=1x^0+288x^125+288x^126+240x^127+435x^128+192x^129+576x^130+288x^131+360x^132+480x^134+144x^135+96x^136+24x^140+288x^141+192x^142+96x^143+108x^144

The gray image is a code over GF(4) with n=176, k=6 and d=125.
This code was found by Heurico 1.16 in 7.25 seconds.