The generator matrix

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

generates a code of length 96 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 266.

Homogenous weight enumerator: w(x)=1x^0+504x^266+648x^267+525x^268+960x^269+2616x^270+2592x^271+1974x^272+2532x^273+5424x^274+4800x^275+3633x^276+4704x^277+8568x^278+8016x^279+5460x^280+5676x^281+12228x^282+10236x^283+7335x^284+7512x^285+14592x^286+12492x^287+8130x^288+8844x^289+16908x^290+12840x^291+8280x^292+8352x^293+14820x^294+11112x^295+6222x^296+5928x^297+9996x^298+7236x^299+3828x^300+3444x^301+4704x^302+2940x^303+1356x^304+984x^305+1476x^306+720x^307+210x^308+168x^309+300x^310+96x^311+84x^312+36x^313+24x^314+27x^316+12x^317+6x^320+15x^324+12x^328+3x^332+3x^336

The gray image is a linear code over GF(4) with n=384, k=9 and d=266.
This code was found by Heurico 1.16 in 448 seconds.