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

generates a code of length 97 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 274.

Homogenous weight enumerator: w(x)=1x^0+996x^274+1260x^276+3348x^278+2676x^280+5388x^282+3840x^284+5604x^286+4170x^288+6084x^290+4164x^292+6792x^294+3909x^296+5160x^298+2964x^300+3912x^302+1857x^304+1848x^306+624x^308+684x^310+123x^312+108x^314+12x^316+12x^318

The gray image is a linear code over GF(4) with n=388, k=8 and d=274.
This code was found by Heurico 1.16 in 51 seconds.