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

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+327x^280+816x^281+516x^282+1104x^283+1404x^284+2424x^285+1416x^286+1836x^287+1995x^288+2712x^289+2028x^290+2376x^291+2565x^292+3516x^293+1944x^294+2604x^295+2817x^296+3348x^297+1956x^298+2484x^299+2514x^300+2700x^301+1716x^302+2028x^303+2097x^304+2760x^305+1248x^306+1632x^307+1524x^308+2028x^309+924x^310+936x^311+816x^312+912x^313+444x^314+312x^315+270x^316+216x^317+96x^318+36x^319+27x^320+60x^321+12x^323+27x^324+12x^325

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 31.6 seconds.