The generator matrix

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

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+675x^280+852x^281+840x^282+2319x^284+2328x^285+1260x^286+3714x^288+3564x^289+1740x^290+4200x^292+3792x^293+1800x^294+4944x^296+3888x^297+2004x^298+4410x^300+3948x^301+1920x^302+3846x^304+3012x^305+1392x^306+2616x^308+1800x^309+852x^310+1317x^312+1092x^313+348x^314+471x^316+228x^317+108x^318+159x^320+72x^321+12x^322+12x^326

The gray image is a linear code over GF(4) with n=396, k=8 and d=280.
This code was found by Heurico 1.16 in 115 seconds.