The generator matrix

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

generates a code of length 99 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 272.

Homogenous weight enumerator: w(x)=1x^0+141x^272+300x^276+405x^280+60x^283+435x^284+420x^287+384x^288+1560x^291+405x^292+3720x^295+303x^296+4332x^299+315x^300+2196x^303+240x^304+231x^308+204x^312+198x^316+129x^320+135x^324+114x^328+66x^332+42x^336+15x^340+18x^344+6x^348+3x^352+3x^356+3x^372

The gray image is a linear code over GF(4) with n=396, k=7 and d=272.
This code was found by Heurico 1.16 in 5.03 seconds.