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

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

Homogenous weight enumerator: w(x)=1x^0+81x^224+174x^228+48x^231+171x^232+432x^235+129x^236+1296x^239+123x^240+1296x^243+84x^244+48x^248+57x^252+30x^256+30x^260+27x^264+30x^268+12x^272+15x^276+6x^284+3x^288+3x^308

The gray image is a code over GF(4) with n=320, k=6 and d=224.
This code was found by Heurico 1.16 in 0.308 seconds.