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

generates a code of length 84 over GR(16,4) who´s minimum homogenous weight is 244.

Homogenous weight enumerator: w(x)=1x^0+384x^244+2064x^248+576x^252+123x^256+192x^260+648x^264+96x^268+12x^272

The gray image is a code over GF(4) with n=336, k=6 and d=244.
This code was found by Heurico 1.16 in 0.305 seconds.