The generator matrix

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

generates a code of length 86 over GR(16,4) who´s minimum homogenous weight is 251.

Homogenous weight enumerator: w(x)=1x^0+420x^251+30x^252+1728x^254+588x^255+105x^256+156x^259+63x^260+45x^264+132x^267+576x^270+180x^271+60x^275+3x^276+9x^280

The gray image is a code over GF(4) with n=344, k=6 and d=251.
This code was found by Heurico 1.16 in 13.5 seconds.