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

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+498x^280+696x^281+852x^282+672x^283+1767x^284+2136x^285+1572x^286+1032x^287+2511x^288+3120x^289+1800x^290+1368x^291+3402x^292+3444x^293+2304x^294+1692x^295+3474x^296+3408x^297+2076x^298+1560x^299+3267x^300+3132x^301+2064x^302+1140x^303+2580x^304+2652x^305+1692x^306+1056x^307+1911x^308+1608x^309+888x^310+480x^311+1095x^312+972x^313+456x^314+180x^315+426x^316+288x^317+84x^318+24x^319+54x^320+48x^321+36x^322+12x^323+3x^324+3x^328

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 65.4 seconds.