The generator matrix

 1  0  1  1  1  1  1  1  1  0  1  1  1  1  0  1  1  1  1  X  1  1  1  1  X  1  1  X  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  X  1  1  1  1  1  0  X a*X a^2*X  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 a*X a*X a*X  X  1  1  1  0 a*X a*X  0  X  1  1 a*X
 0  1  1  a a^2*X+a^2  0 a^2*X+1  a a^2*X+a^2  1  0  a a^2*X+1 a^2*X+a^2  1  X a^2*X+1 X+a a*X+a^2  1  X  1 X+a a*X+a^2  1  X a*X+1  1  0 a^2*X+a a*X+a^2 a^2*X+1 X+a  X a*X X+1 X+a a*X+1 a^2*X+a a*X+1  a  X  1 a^2*X+a a*X a*X+1  1  1 a^2*X+1 a^2*X+a a^2*X+a a^2*X+a^2 a*X+a  1 X+a a*X+1  a a*X+a^2  1 a^2*X+a^2 a*X+a^2 X+a^2 a^2  X  1  1  1  1  0  0 a*X a*X a*X a^2*X X+a^2 X+a^2 a*X+a^2 X+a^2 a^2*X+a^2 a*X+a^2 a^2*X+a^2 X+a^2 X+a^2  1  1  1  1  0 a^2*X a^2*X  1  1  1  1  1  X X+a^2  1
 0  0 a^2*X  0  X  0  X a*X a*X a*X a*X  X a^2*X a^2*X  0 a^2*X  0 a^2*X  0  X  X a*X a*X  X a^2*X a*X  X a*X a^2*X  X  0  X  X a^2*X  0 a^2*X a*X a^2*X  0 a*X a*X a*X  0 a^2*X  X  X a*X  0  0 a^2*X  0 a*X  X  X a^2*X a*X  0 a^2*X a^2*X  X a^2*X  0 a*X  X  X a*X a^2*X  0  0 a*X  X a^2*X  0 a^2*X  X a*X a*X  X  X  0 a^2*X  0 a*X  0  X  X  0 a^2*X  0  X  X a^2*X  0 a*X a^2*X  X  0 a^2*X
 0  0  0  X a*X a*X  0 a*X  X  X  0  X a*X  X  X  0  0  X  X  X  0  0  X  X  X a*X a*X  0 a*X a*X a*X  X a^2*X a^2*X a^2*X  X a^2*X a^2*X a^2*X  X  0 a^2*X  X a^2*X a^2*X a^2*X a^2*X a^2*X a*X a*X  0 a*X  0  0  0 a*X a*X a*X  0 a^2*X a^2*X a^2*X a^2*X a*X a*X a*X a*X a*X  X  X  X  X  0  0 a*X a*X  0  X  0  0  0  X a^2*X  0  0  X a^2*X a^2*X a*X a^2*X a^2*X  X a*X a^2*X a^2*X a*X a^2*X a*X

generates a code of length 98 over F4[X]/(X^2) 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 linear code over GF(4) with n=392, k=6 and d=288.
This code was found by Heurico 1.16 in 86.3 seconds.