The generator matrix

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

generates a code of length 87 over GR(16,4) who´s minimum homogenous weight is 257.

Homogenous weight enumerator: w(x)=1x^0+144x^257+180x^260+480x^261+60x^264+144x^265+6x^268+6x^284+3x^288

The gray image is a code over GF(4) with n=348, k=5 and d=257.
This code was found by Heurico 1.16 in 0.156 seconds.