The generator matrix

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

generates a code of length 88 over GR(16,4) who´s minimum homogenous weight is 257.

Homogenous weight enumerator: w(x)=1x^0+468x^257+612x^258+228x^259+9x^260+480x^261+480x^262+192x^263+21x^264+336x^265+300x^266+84x^267+27x^268+180x^269+84x^270+24x^271+132x^273+120x^274+12x^275+36x^277+36x^278+3x^280+48x^281+72x^282+12x^283+48x^285+24x^286+24x^287+3x^312

The gray image is a code over GF(4) with n=352, k=6 and d=257.
This code was found by Heurico 1.16 in 22.3 seconds.