The generator matrix

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

generates a code of length 96 over F4[X]/(X^2) who´s minimum homogenous weight is 272.

Homogenous weight enumerator: w(x)=1x^0+246x^272+48x^273+168x^274+750x^276+780x^277+348x^278+1074x^280+792x^281+384x^282+1194x^284+1164x^285+672x^286+909x^288+1152x^289+468x^290+1173x^292+1092x^293+588x^294+888x^296+792x^297+312x^298+549x^300+228x^301+120x^302+234x^304+96x^305+12x^306+30x^308+39x^312+21x^316+15x^320+12x^324+15x^328+12x^332+3x^336+3x^340

The gray image is a linear code over GF(4) with n=384, k=7 and d=272.
This code was found by Heurico 1.16 in 2.33 seconds.