The generator matrix

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

generates a code of length 95 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 268.

Homogenous weight enumerator: w(x)=1x^0+360x^268+792x^269+660x^270+612x^271+1725x^272+2016x^273+1560x^274+1080x^275+2856x^276+3048x^277+2124x^278+1476x^279+3255x^280+3168x^281+2208x^282+1608x^283+3285x^284+3444x^285+2100x^286+1416x^287+3282x^288+3636x^289+2100x^290+1392x^291+2832x^292+2640x^293+1584x^294+876x^295+2031x^296+1776x^297+1056x^298+528x^299+1008x^300+708x^301+312x^302+228x^303+339x^304+252x^305+84x^306+24x^309+36x^310+12x^312+3x^316+3x^320

The gray image is a linear code over GF(4) with n=380, k=8 and d=268.
This code was found by Heurico 1.16 in 30.6 seconds.