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

generates a code of length 85 over GR(16,4) who´s minimum homogenous weight is 249.

Homogenous weight enumerator: w(x)=1x^0+432x^249+396x^250+1728x^251+138x^252+180x^254+45x^256+156x^257+45x^260+15x^264+120x^265+180x^266+576x^267+12x^270+60x^273+9x^276+3x^280

The gray image is a code over GF(4) with n=340, k=6 and d=249.
This code was found by Heurico 1.16 in 94.9 seconds.