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

generates a code of length 98 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 282.

Homogenous weight enumerator: w(x)=1x^0+768x^282+852x^283+156x^284+1776x^286+1128x^287+210x^288+1800x^290+1248x^291+168x^292+1536x^294+972x^295+219x^296+1224x^298+588x^299+132x^300+864x^302+588x^303+48x^304+600x^306+408x^307+27x^308+384x^310+276x^311+30x^312+216x^314+72x^315+18x^316+48x^318+12x^319+9x^320+3x^324+3x^328

The gray image is a linear code over GF(4) with n=392, k=7 and d=282.
This code was found by Heurico 1.16 in 83.9 seconds.