The generator matrix

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

generates a code of length 44 over GR(16,4) who´s minimum homogenous weight is 131.

Homogenous weight enumerator: w(x)=1x^0+144x^131+54x^132+48x^135+3x^144+6x^148

The gray image is a code over GF(4) with n=176, k=4 and d=131.
This code was found by Heurico 1.16 in 4.42 seconds.