The generator matrix

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

generates a code of length 98 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 276.

Homogenous weight enumerator: w(x)=1x^0+93x^276+204x^279+477x^280+300x^282+696x^283+861x^284+384x^286+972x^287+1041x^288+492x^290+1020x^291+1104x^292+612x^294+996x^295+1353x^296+660x^298+864x^299+978x^300+408x^302+852x^303+735x^304+180x^306+396x^307+297x^308+36x^310+144x^311+120x^312+27x^316+18x^320+15x^324+12x^328+18x^332+3x^336+9x^340+6x^348

The gray image is a linear code over GF(4) with n=392, k=7 and d=276.
This code was found by Heurico 1.16 in 2.38 seconds.