The generator matrix

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

generates a code of length 99 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 278.

Homogenous weight enumerator: w(x)=1x^0+168x^278+264x^279+507x^280+456x^281+1188x^282+888x^283+1281x^284+1200x^285+2688x^286+1248x^287+1998x^288+1584x^289+3336x^290+1788x^291+2616x^292+1824x^293+4044x^294+2028x^295+2526x^296+2088x^297+3792x^298+1860x^299+2583x^300+1968x^301+3888x^302+1752x^303+2253x^304+1680x^305+3048x^306+1428x^307+1554x^308+1008x^309+1620x^310+708x^311+771x^312+336x^313+636x^314+276x^315+177x^316+144x^317+168x^318+48x^319+51x^320+21x^324+6x^328+12x^332+6x^336+9x^340+3x^344+3x^348+3x^352+3x^360

The gray image is a linear code over GF(4) with n=396, k=8 and d=278.
This code was found by Heurico 1.16 in 30.7 seconds.