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

generates a code of length 99 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 280.

Homogenous weight enumerator: w(x)=1x^0+69x^280+72x^282+336x^283+606x^284+324x^286+768x^287+1197x^288+444x^290+960x^291+1095x^292+528x^294+948x^295+978x^296+492x^298+1152x^299+1167x^300+660x^302+996x^303+906x^304+420x^306+576x^307+687x^308+120x^310+348x^311+258x^312+12x^314+48x^315+90x^316+12x^319+36x^320+30x^324+18x^328+6x^332+6x^336+6x^340+6x^348+3x^360+3x^364

The gray image is a linear code over GF(4) with n=396, k=7 and d=280.
This code was found by Heurico 1.16 in 2.43 seconds.