The generator matrix

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

generates a code of length 78 over GR(16,4) who´s minimum homogenous weight is 220.

Homogenous weight enumerator: w(x)=1x^0+717x^220+1743x^224+2796x^228+2640x^232+3600x^236+2691x^240+1578x^244+432x^248+72x^252+36x^256+36x^260+24x^268+9x^272+6x^276+3x^284

The gray image is a code over GF(4) with n=312, k=7 and d=220.
This code was found by Heurico 1.16 in 52.7 seconds.