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

generates a code of length 98 over GR(16,4) who´s minimum homogenous weight is 288.

Homogenous weight enumerator: w(x)=1x^0+1395x^288+1152x^290+576x^296+396x^304+384x^306+186x^312+6x^328

The gray image is a code over GF(4) with n=392, k=6 and d=288.
This code was found by Heurico 1.16 in 85.9 seconds.