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  1 aX  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  X aX+1 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  0 X+1 aX+a+1 aX+a X+a  0
 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 a+1  1 X+1  1  X X+1

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+564x^277+1008x^278+516x^279+66x^280+2376x^281+2592x^282+1020x^283+153x^284+3636x^285+3816x^286+1368x^287+120x^288+4200x^289+4404x^290+1380x^291+174x^292+4332x^293+4596x^294+1560x^295+147x^296+4368x^297+3984x^298+1260x^299+162x^300+3684x^301+3624x^302+1044x^303+123x^304+2532x^305+2244x^306+744x^307+30x^308+1404x^309+1044x^310+264x^311+39x^312+492x^313+312x^314+60x^315+9x^316+60x^317+24x^318

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 31.6 seconds.