The generator matrix

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

generates a code of length 95 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 266.

Homogenous weight enumerator: w(x)=1x^0+120x^266+420x^267+345x^268+636x^269+888x^270+1308x^271+945x^272+1200x^273+1500x^274+2436x^275+1755x^276+1920x^277+1932x^278+3000x^279+2208x^280+2316x^281+2448x^282+3648x^283+2256x^284+2676x^285+2820x^286+3420x^287+1821x^288+3012x^289+2220x^290+3324x^291+1779x^292+2004x^293+1920x^294+2148x^295+1431x^296+1140x^297+1104x^298+1380x^299+564x^300+432x^301+300x^302+360x^303+96x^304+12x^305+96x^306+24x^307+33x^308+12x^309+12x^310+36x^311+18x^312+15x^316+9x^320+15x^324+9x^328+6x^332+6x^336

The gray image is a linear code over GF(4) with n=380, k=8 and d=266.
This code was found by Heurico 1.16 in 31.7 seconds.