The generator matrix

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

generates a code of length 86 over GR(16,4) who´s minimum homogenous weight is 244.

Homogenous weight enumerator: w(x)=1x^0+147x^244+36x^247+213x^248+288x^251+135x^252+840x^255+144x^256+1152x^259+87x^260+756x^263+84x^264+36x^268+39x^272+33x^276+27x^280+9x^284+21x^288+18x^292+12x^296+12x^300+3x^304+3x^324

The gray image is a code over GF(4) with n=344, k=6 and d=244.
This code was found by Heurico 1.16 in 0.516 seconds.