The generator matrix

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

generates a code of length 98 over F4[X]/(X^2) who´s minimum homogenous weight is 272.

Homogenous weight enumerator: w(x)=1x^0+588x^272+624x^273+624x^274+936x^275+2613x^276+2856x^277+2220x^278+2184x^279+5064x^280+5604x^281+3720x^282+3816x^283+8844x^284+8220x^285+5328x^286+5400x^287+11799x^288+12084x^289+7368x^290+6624x^291+14838x^292+12744x^293+8928x^294+7488x^295+15324x^296+14016x^297+8700x^298+6924x^299+14247x^300+11580x^301+6600x^302+5772x^303+10170x^304+7284x^305+3852x^306+2640x^307+4815x^308+3720x^309+1428x^310+1008x^311+1470x^312+900x^313+300x^314+180x^315+249x^316+240x^317+72x^318+36x^319+30x^320+12x^322+30x^324+9x^328+6x^332+6x^336+6x^340+3x^344

The gray image is a linear code over GF(4) with n=392, k=9 and d=272.
This code was found by Heurico 1.16 in 418 seconds.