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

generates a code of length 97 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 272.

Homogenous weight enumerator: w(x)=1x^0+198x^272+288x^273+96x^274+852x^275+1389x^276+1080x^277+216x^278+1836x^279+2592x^280+1560x^281+432x^282+2940x^283+3237x^284+2160x^285+540x^286+3540x^287+3849x^288+2532x^289+480x^290+3576x^291+4794x^292+2640x^293+348x^294+3288x^295+4476x^296+2256x^297+420x^298+2568x^299+2562x^300+1692x^301+276x^302+1956x^303+1809x^304+756x^305+168x^306+708x^307+456x^308+288x^309+60x^310+228x^311+144x^312+96x^313+36x^314+12x^315+18x^316+12x^317+30x^320+15x^324+12x^328+3x^332+9x^336+6x^340

The gray image is a linear code over GF(4) with n=388, k=8 and d=272.
This code was found by Heurico 1.16 in 32.4 seconds.