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

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

Homogenous weight enumerator: w(x)=1x^0+648x^224+636x^225+888x^226+372x^227+1974x^228+2208x^229+1980x^230+588x^231+3303x^232+2760x^233+2664x^234+708x^235+3870x^236+3636x^237+2928x^238+888x^239+4269x^240+3384x^241+3096x^242+744x^243+4116x^244+3348x^245+2556x^246+744x^247+3504x^248+2388x^249+1824x^250+384x^251+1677x^252+1272x^253+768x^254+132x^255+624x^256+288x^257+168x^258+48x^259+72x^260+48x^261+24x^262+3x^264+3x^268

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 29.2 seconds.