The generator matrix

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

generates a code of length 98 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 276.

Homogenous weight enumerator: w(x)=1x^0+333x^276+948x^277+360x^278+156x^279+1302x^280+2688x^281+672x^282+276x^283+2301x^284+4140x^285+1332x^286+480x^287+2616x^288+4908x^289+1572x^290+468x^291+3168x^292+5520x^293+1548x^294+588x^295+3390x^296+5880x^297+1524x^298+444x^299+2505x^300+4596x^301+1020x^302+360x^303+2316x^304+2868x^305+732x^306+252x^307+1065x^308+1572x^309+348x^310+48x^311+330x^312+528x^313+108x^314+48x^316+120x^317+24x^320+24x^321+21x^324+12x^328+12x^332+9x^336+3x^356

The gray image is a linear code over GF(4) with n=392, k=8 and d=276.
This code was found by Heurico 1.16 in 45.9 seconds.