The generator matrix

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

generates a code of length 97 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 268.

Homogenous weight enumerator: w(x)=1x^0+192x^268+384x^269+252x^270+696x^271+1578x^272+2520x^273+1368x^274+2760x^275+4149x^276+5112x^277+2760x^278+4500x^279+6612x^280+8148x^281+3600x^282+6804x^283+9135x^284+11148x^285+5112x^286+9636x^287+12534x^288+14328x^289+6516x^290+11208x^291+13941x^292+15276x^293+6408x^294+10320x^295+12984x^296+13164x^297+5316x^298+8400x^299+8925x^300+9588x^301+3228x^302+4872x^303+5709x^304+4584x^305+1764x^306+1728x^307+1641x^308+1548x^309+480x^310+492x^311+315x^312+168x^313+60x^314+12x^315+48x^316+48x^317+12x^319+21x^320+15x^324+3x^328+18x^332+3x^336

The gray image is a linear code over GF(4) with n=388, k=9 and d=268.
This code was found by Heurico 1.16 in 454 seconds.