The generator matrix

 1  0  0  0  1  1  1  1  1  1  1  1  1 aX  1  1  X  1  1 (a+1)X  1  1 (a+1)X  1  1  1  1  1  1  0  1  1  0 aX  0  1  X  1 aX  1  1  1  1  X  1  1  1  1  1  1  1  1  1  1  X  1  1 (a+1)X  1 (a+1)X  0 aX  1  1 (a+1)X  1  1  1  1  1  X  1  1 (a+1)X  1  1  1  1  1 aX aX  1  1  1  1 aX  1  1  1  1  1  1  1  1  1  1  1  1
 0  1  0  0  0  0 (a+1)X (a+1)X (a+1)X aX  0 (a+1)X aX  1 X+1 (a+1)X+1  1 aX+a+1 X+1  1  1 (a+1)X+a  1  1 X+a (a+1)X+a aX+a aX a+1  1 (a+1)X+1 aX+a  1  0  1  a  1 X+1  1 aX+a (a+1)X+1 (a+1)X+a aX+1  1 X+1 (a+1)X+1 a+1  1 X+1 (a+1)X+a a+1 aX aX+a+1 (a+1)X+a+1  0 (a+1)X+a+1  X  1 aX+a  1 (a+1)X (a+1)X X+a (a+1)X+a  1  a aX+a (a+1)X+1 aX+a+1  a  1 aX+a+1 X+a  1 X+1  1 aX+a+1 aX+a+1 (a+1)X  1  1 X+a+1 (a+1)X (a+1)X+a+1  X  1 X+a  1  X aX+1 (a+1)X (a+1)X+1 (a+1)X+a+1 aX+1  a (a+1)X+1 aX+a+1 a+1
 0  0  1  0  0  X  0 (a+1)X+1  a (a+1)X+1  a aX+1 (a+1)X+a+1  1  X aX+a+1 aX+a+1 (a+1)X+a+1  1 (a+1)X+1 (a+1)X  1 X+a+1 (a+1)X+a X+1 aX+a+1 (a+1)X (a+1)X+a  X aX+1 aX+a aX+a  a  1  0 (a+1)X+a+1  0 aX+1 (a+1)X+a  a aX+a+1 X+a aX  a aX+a+1 aX+1  X  a (a+1)X aX+a X+a a+1 (a+1)X+1  1  1  a aX+1 (a+1)X+a+1  1 X+a  1  X aX+a  0 (a+1)X+1 X+a+1 (a+1)X (a+1)X+1  a (a+1)X+1 X+a+1  0 (a+1)X+a+1  1  1  0 a+1 (a+1)X (a+1)X+a aX+a (a+1)X+a aX+a+1 aX (a+1)X+1  a aX aX+1  X  1 aX a+1  1 (a+1)X+a a+1  0 (a+1)X+1  a (a+1)X
 0  0  0  1  1 (a+1)X+a a+1 a+1 X+a+1  a  X (a+1)X+1  0 (a+1)X+a+1 (a+1)X+a+1 X+1 (a+1)X aX  a X+a aX+1  0  a (a+1)X+1 (a+1)X+a+1  1 X+a aX+1 a+1 X+1  X aX+a a+1 (a+1)X+a+1 X+a+1  a  1 aX+a+1 X+1 (a+1)X+1  0 (a+1)X+a+1  X aX aX+a+1  1 X+1 (a+1)X+a+1 X+a  0  X  1 (a+1)X (a+1)X+a+1  a aX+a+1 X+a+1 aX+a+1  1 X+a (a+1)X+1  1  1 X+a+1  X aX X+a aX X+1 aX+a  1 aX aX (a+1)X aX+1 a+1 X+a  X  a  1  0 (a+1)X+a+1  X aX+a (a+1)X+a+1 (a+1)X X+1  X  0 (a+1)X+a X+1  1 (a+1)X  a X+a+1 X+a (a+1)X+a+1 X+a
 0  0  0  0 (a+1)X  X aX  0  X (a+1)X  0  0  X  0  0  0  X aX  0 aX  X aX (a+1)X aX  X  X aX  0 (a+1)X  0  X (a+1)X aX  X aX (a+1)X  0 aX (a+1)X (a+1)X aX  0  X aX  X  0 aX (a+1)X (a+1)X  0  0 (a+1)X  X aX (a+1)X  X (a+1)X  0 (a+1)X (a+1)X aX  X  0  0 (a+1)X  X  0 aX (a+1)X  0 (a+1)X  0 (a+1)X  X (a+1)X  X (a+1)X aX aX aX  0 aX (a+1)X aX  0 (a+1)X aX (a+1)X (a+1)X aX  0  0 aX (a+1)X aX aX  X aX

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

Homogenous weight enumerator: w(x)=1x^0+450x^272+888x^273+792x^274+672x^275+2091x^276+3348x^277+2832x^278+1440x^279+4761x^280+6888x^281+4884x^282+2496x^283+7212x^284+9060x^285+7056x^286+3816x^287+10320x^288+12420x^289+8772x^290+4908x^291+13014x^292+15516x^293+10788x^294+5784x^295+13509x^296+16572x^297+10404x^298+5436x^299+12249x^300+13620x^301+8580x^302+3288x^303+8355x^304+8580x^305+4740x^306+2148x^307+4377x^308+3984x^309+1980x^310+648x^311+1107x^312+1116x^313+552x^314+84x^315+297x^316+168x^317+60x^318+24x^320+15x^324+18x^328+6x^332+6x^336+3x^340+9x^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 465 seconds.