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

generates a code of length 99 over F4[X]/(X^2) who´s minimum homogenous weight is 280.

Homogenous weight enumerator: w(x)=1x^0+468x^280+612x^281+924x^282+660x^283+1659x^284+1680x^285+2220x^286+1164x^287+2985x^288+1980x^289+2568x^290+1572x^291+3699x^292+2400x^293+3048x^294+1332x^295+3720x^296+2412x^297+2892x^298+1536x^299+3363x^300+1944x^301+2640x^302+1164x^303+2943x^304+2184x^305+2148x^306+936x^307+2217x^308+1344x^309+1164x^310+564x^311+1113x^312+552x^313+684x^314+180x^315+294x^316+216x^317+96x^318+96x^319+63x^320+36x^321+48x^322+12x^323+3x^328

The gray image is a linear code over GF(4) with n=396, k=8 and d=280.
This code was found by Heurico 1.16 in 34.1 seconds.