The generator matrix

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

generates a code of length 80 over GR(16,4) who´s minimum homogenous weight is 224.

Homogenous weight enumerator: w(x)=1x^0+813x^224+588x^225+624x^226+744x^227+2628x^228+1260x^229+1284x^230+1308x^231+3927x^232+1992x^233+1620x^234+1956x^235+4968x^236+2484x^237+1848x^238+1776x^239+5541x^240+2412x^241+1848x^242+2052x^243+4905x^244+2376x^245+1740x^246+1704x^247+4068x^248+1692x^249+1212x^250+840x^251+2538x^252+720x^253+408x^254+348x^255+735x^256+276x^257+168x^258+24x^259+81x^260+24x^261+3x^264

The gray image is a code over GF(4) with n=320, k=8 and d=224.
This code was found by Heurico 1.16 in 58.7 seconds.