The generator matrix

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

generates a code of length 98 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 281.

Homogenous weight enumerator: w(x)=1x^0+456x^281+276x^282+588x^283+174x^284+1392x^285+528x^286+936x^287+183x^288+1416x^289+564x^290+864x^291+186x^292+1284x^293+648x^294+708x^295+129x^296+1140x^297+384x^298+444x^299+177x^300+684x^301+252x^302+588x^303+102x^304+600x^305+228x^306+264x^307+36x^308+420x^309+96x^310+156x^311+33x^312+228x^313+84x^314+48x^315+3x^316+60x^317+12x^318+12x^319

The gray image is a linear code over GF(4) with n=392, k=7 and d=281.
This code was found by Heurico 1.16 in 1.6 seconds.