The generator matrix

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

generates a code of length 44 over GR(16,4) who´s minimum homogenous weight is 128.

Homogenous weight enumerator: w(x)=1x^0+189x^128+768x^132+63x^144+3x^176

The gray image is a code over GF(4) with n=176, k=5 and d=128.
This code was found by Heurico 1.16 in 6.39 seconds.