The generator matrix

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

generates a code of length 96 over F4[X]/(X^2) who´s minimum homogenous weight is 269.

Homogenous weight enumerator: w(x)=1x^0+132x^269+252x^270+396x^271+534x^272+1284x^273+1008x^274+1260x^275+1158x^276+2112x^277+1776x^278+1752x^279+1755x^280+2784x^281+2052x^282+2148x^283+2247x^284+3432x^285+2496x^286+2916x^287+2130x^288+3408x^289+2652x^290+2304x^291+2175x^292+3804x^293+2340x^294+2340x^295+1698x^296+2400x^297+1596x^298+1332x^299+1128x^300+1500x^301+828x^302+720x^303+261x^304+588x^305+276x^306+156x^307+102x^308+60x^309+84x^310+36x^311+48x^312+36x^316+12x^320+9x^324+6x^328+3x^332+6x^340+3x^344

The gray image is a linear code over GF(4) with n=384, k=8 and d=269.
This code was found by Heurico 1.16 in 33.3 seconds.