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

generates a code of length 99 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 288.

Homogenous weight enumerator: w(x)=1x^0+282x^288+312x^291+981x^292+576x^293+264x^295+384x^296+303x^300+174x^304+72x^307+252x^308+192x^309+120x^311+84x^312+90x^316+3x^320+3x^324+3x^332

The gray image is a linear code over GF(4) with n=396, k=6 and d=288.
This code was found by Heurico 1.16 in 0.3 seconds.