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

generates a code of length 96 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 271.

Homogenous weight enumerator: w(x)=1x^0+756x^271+594x^272+156x^273+624x^274+2604x^275+1968x^276+372x^277+1188x^278+4428x^279+2598x^280+384x^281+1404x^282+5484x^283+3138x^284+444x^285+1440x^286+5316x^287+3285x^288+612x^289+1644x^290+5148x^291+2904x^292+408x^293+1200x^294+4524x^295+2409x^296+396x^297+960x^298+3384x^299+1590x^300+240x^301+528x^302+1548x^303+705x^304+36x^305+156x^306+516x^307+228x^308+24x^309+60x^310+84x^311+21x^312+12x^314+12x^316+3x^320

The gray image is a linear code over GF(4) with n=384, k=8 and d=271.
This code was found by Heurico 1.16 in 28.8 seconds.