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

generates a code of length 44 over GR(16,4) who´s minimum homogenous weight is 120.

Homogenous weight enumerator: w(x)=1x^0+270x^120+192x^126+312x^128+1152x^130+1728x^134+210x^136+138x^144+66x^152+21x^160+6x^168

The gray image is a code over GF(4) with n=176, k=6 and d=120.
This code was found by Heurico 1.16 in 83.3 seconds.