The generator matrix

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

generates a code of length 93 over F4[X]/(X^2) who´s minimum homogenous weight is 257.

Homogenous weight enumerator: w(x)=1x^0+552x^257+588x^258+888x^259+765x^260+2244x^261+2652x^262+2208x^263+1806x^264+4836x^265+5496x^266+3876x^267+2583x^268+8616x^269+7944x^270+6540x^271+4302x^272+12060x^273+11724x^274+8712x^275+5805x^276+16092x^277+13836x^278+9744x^279+6435x^280+16548x^281+14484x^282+9096x^283+6144x^284+15660x^285+11628x^286+7692x^287+3984x^288+9996x^289+7272x^290+4512x^291+2061x^292+4224x^293+3336x^294+1512x^295+657x^296+1128x^297+756x^298+468x^299+171x^300+204x^301+156x^302+48x^303+39x^304+12x^308+18x^312+15x^316+6x^320+9x^324+3x^332

The gray image is a linear code over GF(4) with n=372, k=9 and d=257.
This code was found by Heurico 1.16 in 432 seconds.