The generator matrix

 1  0  1  1  1  1  1  1  1  0  1  1  1  0  1  1  1  1  1  2  1  1 2a  1  1  1  1  1  0  1  1 2a  1  1  1  1 2a+2  1  1  1  1 2a+2  1  1  1  1  1  2  1  1 2a  1  1  1  2  1  0  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 2a  1  1  1 2a  1  1  1
 0  1  1  a 3a+3  0 2a+3 a+1  a  1  0 2a+3  a  1 a+1  2 a+1 a+2 2a+3  1 a+1  a  1  0  a 3a+3 2a+3  3  1 2a+2 2a+3  1 3a  0 a+3  3  1 3a+2  3  3 a+3  1 a+3 2a a+3 a+3  2  1 a+1  3  1 2a+2 2a 3a  1 3a+3  1 2a+1 2a+1 2a+3 3a+1 2a+3 3a+2 3a+2  0 2a 2a+2  3 3a+2 2a+2  1 3a+3  1 3a 3a 3a  1 2a+2 a+2  0
 0  0 2a+2  0  0  0  2  2  2  2  2  2 2a+2 2a+2 2a  2 2a 2a+2 2a+2  0 2a+2 2a+2 2a 2a+2 2a  0 2a  2  2 2a+2 2a 2a+2  0 2a+2 2a  0 2a 2a  2 2a  2 2a+2 2a+2 2a 2a  0  0  0  2  2  2  2  2 2a 2a  0  0 2a+2 2a+2 2a 2a  0 2a 2a+2 2a  2  2 2a  0  0 2a+2 2a+2  2 2a+2  0 2a+2 2a+2  0 2a  0
 0  0  0  2  0  2 2a+2  0  2 2a+2  2  0 2a 2a+2  0 2a+2  0  0 2a 2a  2  2 2a+2 2a+2  0 2a 2a  0 2a+2  2  2 2a  2  2  0  2 2a+2  2  0  2  2  2 2a+2  0 2a+2  0  0 2a 2a  2  0 2a+2  0 2a  2 2a+2 2a+2  2 2a  0  2 2a 2a+2 2a+2 2a+2  0  2 2a+2 2a+2  0  2 2a+2 2a+2 2a 2a 2a+2  2  2  2  2
 0  0  0  0 2a+2 2a+2  2 2a+2 2a  0 2a+2  2  2 2a  2 2a 2a  2 2a+2 2a+2  0 2a+2 2a+2  2  0 2a+2  0 2a+2 2a+2 2a  2  2 2a  2 2a+2  2  0 2a 2a  0 2a+2 2a  0  2  0 2a 2a+2  2 2a  2  0 2a+2  0  2  2 2a 2a+2  0  0  0  0 2a 2a+2 2a  2 2a  2  2 2a  2 2a 2a+2 2a 2a 2a+2 2a+2  0 2a  2 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+99x^224+204x^225+384x^227+477x^228+636x^229+672x^231+471x^232+804x^233+1020x^235+726x^236+1032x^237+1164x^239+669x^240+1212x^241+1272x^243+714x^244+1068x^245+1176x^247+567x^248+876x^249+396x^251+204x^252+240x^253+60x^255+42x^256+72x^257+42x^260+6x^264+21x^268+18x^272+15x^276+12x^280+9x^284+3x^288

The gray image is a code over GF(4) with n=320, k=7 and d=224.
This code was found by Heurico 1.16 in 1.87 seconds.