The generator matrix

 1  0  0  0  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 a^2*X  1  1  0  1  1 a*X  1  1 a*X  1  1  X  0  1  1  1  1  1  1  1  0  1 a*X  X  1  0  1  1  1  X  X  1  1  1  1 a*X  X  0  1 a^2*X  1  1  0  1  1  1  1  1  1  1  1  1  1 a*X  1  0  1  1  1  1  1  X  1  1  1  X  X  1  1  1  1
 0  1  0  0 a^2*X a*X a^2*X  X  X  X  1 a^2*X+a a^2 a^2*X+1  1  a X+1 a*X+a^2 a*X+a a^2*X+a^2 a^2*X+a a^2 X+a^2 a*X+a^2 a*X  1 a*X+1 X+a^2  1  a a*X a*X  1 a^2*X+1  1 a^2*X+1 a^2*X+a  0  1 a*X+a^2  a a^2*X+a a^2*X a^2*X+1 X+a^2 a^2*X+a  1  1  1  1  0  1 a*X+1 a^2 a^2*X+a^2  1  1 a^2*X+a^2 X+a^2 a*X+a a*X+a  1  1  X a*X+a  1 a^2*X  a  1 a*X+a^2 X+a  a  a a*X+a a^2*X  0 a*X+a^2 a*X X+1  1 a*X  0 X+a^2  0 a*X+1  1 a^2*X+a^2  1 a^2*X+1 X+a^2 a^2  1  X a*X a*X+1  0  0
 0  0  1  0  0  X  X a^2*X+1  a a^2*X+a^2 a*X  X a^2*X a^2*X  0 X+a X+1 a^2*X  1 a*X+a^2 a^2*X X+a  1  a a^2*X+1  1 X+a^2 X+a^2  1 a*X+1 a*X+a^2  1 X+a^2  1 a*X+a a^2*X+a^2 a*X+a^2  1 X+a  1 a*X a^2 a^2*X+a X+1 a^2*X+1 a*X+a  a a^2 a*X+a^2 a*X+a^2 a*X+a^2 a^2*X+1 a*X+a a^2 a*X a^2 a*X+1  X a^2*X+a  a X+a a^2*X a*X+a  1 a^2*X+a^2 a*X X+a a^2 a*X+1  0 a*X+a  1 X+1 a*X+1 X+1  X a^2*X+a a^2*X+a^2  a a*X a*X+1  1  a X+a^2 X+a a^2  a  a X+a X+a  a X+1  1 X+a^2 a*X+1 a*X a*X+1
 0  0  0  1  1 a^2*X+a a^2*X+a^2 a^2*X+a^2 a^2 a*X+a^2 X+a^2 X+a^2 X+a^2 a^2*X+a X+1  a X+a  1 a*X+a a^2*X+1 a^2*X+1 a^2*X+a a*X  X a*X+a a*X+a  X X+a a^2 a^2*X a*X+1 a*X+a  1  X a^2*X+a^2 a*X+a a^2*X+a^2 a*X+1 a*X a^2*X+a^2 X+a a^2*X X+1 a*X+1  1  0  a a^2 a^2*X+1  0  X a^2*X a*X+1  0 a*X+a X+a^2 a*X+1 a^2*X X+a^2 X+a X+a^2  1 a^2*X+1 a*X+a^2 a*X+a X+a  0 a*X+1 a^2*X+a X+a a*X+1 X+1 X+a^2 X+a a*X+1  1 a^2*X+1 X+a a^2*X a*X+a^2  0 a*X+1 a^2*X+a a^2*X X+a a*X+a a^2*X+a X+1  1 X+1 X+1 a^2  0 X+1 X+a^2 a^2*X+1  a

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

Homogenous weight enumerator: w(x)=1x^0+468x^274+672x^275+849x^276+600x^277+1944x^278+1920x^279+1524x^280+1128x^281+2424x^282+3216x^283+2238x^284+1596x^285+2820x^286+3432x^287+2385x^288+1392x^289+3132x^290+3468x^291+2382x^292+1392x^293+3180x^294+3300x^295+2109x^296+1440x^297+2652x^298+2772x^299+1698x^300+888x^301+2016x^302+1704x^303+1068x^304+588x^305+936x^306+816x^307+489x^308+180x^309+300x^310+144x^311+105x^312+12x^313+84x^314+48x^315+12x^318+12x^319

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 33.4 seconds.