The generator matrix

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

generates a code of length 97 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 276.

Homogenous weight enumerator: w(x)=1x^0+243x^276+336x^277+240x^278+792x^280+852x^281+420x^282+1167x^284+1020x^285+468x^286+1185x^288+912x^289+492x^290+1152x^292+888x^293+624x^294+1251x^296+1056x^297+444x^298+876x^300+636x^301+276x^302+315x^304+336x^305+84x^306+75x^308+96x^309+24x^310+21x^312+12x^313+12x^316+21x^320+12x^324+18x^328+9x^332+6x^336+3x^340+6x^344+3x^356

The gray image is a linear code over GF(4) with n=388, k=7 and d=276.
This code was found by Heurico 1.16 in 6.33 seconds.