The generator matrix

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

generates a code of length 97 over F4[X]/(X^2) who´s minimum homogenous weight is 284.

Homogenous weight enumerator: w(x)=1x^0+900x^284+1476x^288+828x^292+300x^296+216x^300+144x^304+84x^308+60x^312+84x^316+3x^320

The gray image is a linear code over GF(4) with n=388, k=6 and d=284.
This code was found by Heurico 1.16 in 0.625 seconds.