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

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+888x^274+576x^275+693x^276+540x^277+2244x^278+1764x^279+1341x^280+828x^281+3168x^282+2640x^283+2046x^284+780x^285+4020x^286+2916x^287+1980x^288+984x^289+4488x^290+3012x^291+2376x^292+888x^293+4776x^294+2844x^295+2253x^296+828x^297+3684x^298+2268x^299+1206x^300+840x^301+2664x^302+1524x^303+819x^304+288x^305+1212x^306+612x^307+519x^308+108x^309+456x^310+264x^311+54x^312+48x^313+48x^314+12x^315+24x^316+12x^317

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 55.9 seconds.