The generator matrix

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

generates a code of length 97 over F4[X]/(X^2) who´s minimum homogenous weight is 269.

Homogenous weight enumerator: w(x)=1x^0+468x^269+516x^270+1128x^271+966x^272+2304x^273+2460x^274+2484x^275+2454x^276+4788x^277+4536x^278+4956x^279+3951x^280+7572x^281+7128x^282+8112x^283+5841x^284+10692x^285+9132x^286+10512x^287+7164x^288+13104x^289+11844x^290+12024x^291+8925x^292+13608x^293+11832x^294+11184x^295+7926x^296+12204x^297+10332x^298+8820x^299+5661x^300+9000x^301+6384x^302+5736x^303+2985x^304+4344x^305+2592x^306+2028x^307+984x^308+1500x^309+696x^310+564x^311+138x^312+216x^313+108x^314+36x^315+51x^316+72x^317+24x^318+15x^320+18x^324+3x^328+9x^332+3x^336+9x^340

The gray image is a linear code over GF(4) with n=388, k=9 and d=269.
This code was found by Heurico 1.16 in 698 seconds.