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

generates a code of length 76 over GR(16,4) who´s minimum homogenous weight is 220.

Homogenous weight enumerator: w(x)=1x^0+72x^220+252x^224+336x^228+324x^232+24x^236+12x^240+3x^288

The gray image is a code over GF(4) with n=304, k=5 and d=220.
This code was found by Heurico 1.16 in 0.078 seconds.