The generator matrix

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

generates a code of length 96 over F4[X]/(X^2) who´s minimum homogenous weight is 266.

Homogenous weight enumerator: w(x)=1x^0+684x^266+1554x^268+4140x^270+5052x^272+8496x^274+8658x^276+13644x^278+12489x^280+19944x^282+17802x^284+24744x^286+20334x^288+25896x^290+20256x^292+22884x^294+14892x^296+16536x^298+9309x^300+7716x^302+3258x^304+2352x^306+888x^308+408x^310+99x^312+12x^314+54x^316+3x^320+30x^324+9x^332

The gray image is a linear code over GF(4) with n=384, k=9 and d=266.
This code was found by Heurico 1.16 in 413 seconds.