The generator matrix

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

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+804x^287+297x^288+984x^291+312x^292+516x^295+216x^296+300x^299+108x^300+168x^303+18x^304+132x^307+42x^308+72x^311+72x^315+12x^316+24x^319+12x^320+3x^324+3x^356

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 1.3 seconds.