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

generates a code of length 98 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 277.

Homogenous weight enumerator: w(x)=1x^0+480x^277+864x^278+744x^279+435x^280+1848x^281+2328x^282+1584x^283+1008x^284+2604x^285+2772x^286+2232x^287+1059x^288+3300x^289+3288x^290+2820x^291+1143x^292+3552x^293+3540x^294+2376x^295+1167x^296+3492x^297+2928x^298+2304x^299+993x^300+2724x^301+2628x^302+1692x^303+777x^304+1968x^305+1848x^306+1080x^307+393x^308+1212x^309+1020x^310+396x^311+174x^312+288x^313+264x^314+132x^315+15x^316+36x^317+24x^318+3x^320

The gray image is a linear code over GF(4) with n=392, k=8 and d=277.
This code was found by Heurico 1.16 in 32.8 seconds.