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

generates a code of length 56 over GR(16,4) who´s minimum homogenous weight is 166.

Homogenous weight enumerator: w(x)=1x^0+132x^166+33x^168+48x^170+24x^172+3x^176+12x^182+3x^184

The gray image is a code over GF(4) with n=224, k=4 and d=166.
This code was found by Heurico 1.16 in 0.032 seconds.