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

generates a code of length 98 over F4[X]/(X^2) who´s minimum homogenous weight is 277.

Homogenous weight enumerator: w(x)=1x^0+516x^277+420x^278+876x^279+915x^280+1944x^281+1572x^282+1584x^283+1710x^284+2592x^285+2244x^286+2412x^287+1860x^288+3444x^289+2316x^290+2388x^291+2325x^292+3216x^293+2424x^294+2460x^295+2289x^296+3336x^297+2472x^298+2232x^299+1815x^300+2892x^301+1968x^302+1644x^303+1221x^304+2040x^305+1164x^306+1128x^307+795x^308+1032x^309+612x^310+492x^311+300x^312+420x^313+156x^314+108x^315+75x^316+72x^317+12x^318+36x^319+6x^320

The gray image is a linear code over GF(4) with n=392, k=8 and d=277.
This code was found by Heurico 1.16 in 32.5 seconds.