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

generates a code of length 99 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 290.

Homogenous weight enumerator: w(x)=1x^0+588x^290+576x^291+108x^292+672x^294+444x^295+75x^296+504x^298+192x^299+12x^300+204x^302+108x^303+3x^304+156x^306+84x^307+21x^308+72x^310+48x^311+30x^312+36x^314+36x^315+36x^318+24x^319+36x^322+24x^323+3x^324+3x^328

The gray image is a linear code over GF(4) with n=396, k=6 and d=290.
This code was found by Heurico 1.16 in 3.45 seconds.