The generator matrix

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

generates a code of length 98 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 287.

Homogenous weight enumerator: w(x)=1x^0+528x^287+63x^288+1728x^290+360x^291+60x^292+216x^295+81x^296+120x^299+36x^300+120x^303+576x^306+144x^307+6x^312+48x^315+9x^328

The gray image is a linear code over GF(4) with n=392, k=6 and d=287.
This code was found by Heurico 1.16 in 23.1 seconds.