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 a^2*X  1  1 a^2*X a^2*X  X
 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 a*X a*X a*X+a  0  1  X
 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  1 a^2*X+a^2 a^2*X+a^2  1 a^2*X+1  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*X a^2*X+a^2 X+a^2 a^2*X+1 a*X+a^2 a*X+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+564x^274+648x^275+582x^276+696x^277+2028x^278+1968x^279+1305x^280+1200x^281+3048x^282+3048x^283+1767x^284+1464x^285+3144x^286+3600x^287+1815x^288+1332x^289+3804x^290+3600x^291+1809x^292+1416x^293+3540x^294+3132x^295+1899x^296+1332x^297+3048x^298+2796x^299+1407x^300+960x^301+2244x^302+1644x^303+822x^304+552x^305+1212x^306+852x^307+309x^308+204x^309+324x^310+168x^311+54x^312+48x^313+84x^314+48x^315+6x^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 32.4 seconds.