The generator matrix

 1  0  1  1  1  1  1  1  1  0  1  1  1  0  1  1  1  1  1  X  1  1 a*X  1  1  1  1  1  0  1  1  1  1  1 a^2*X  1 a*X  1  1  1  1  1  1 a*X  1 a*X  1  1  X  1  1  X  1  1  X  1  1  1  1  1  1  0  1  1  1  1  1  1  0 a^2*X a^2*X  0  1  1  1  X  1  1  1  1  1 a^2*X  1  1  1  1  1  1  1  1  0  1  1  1  1 a^2*X  1  1  1
 0  1  1  a a^2  0 a^2*X+1 a^2*X+a^2  a  1  0 a^2*X+1  a  1 a^2*X+a^2  X a^2*X+a^2 X+a a^2*X+1  1 a^2*X+a^2  a  1  1 a*X+a a*X+a^2  0 X+a  1 a^2*X+a^2 a*X a^2*X+1 X+a  0  1 a^2*X+1  1 a*X+a^2 X+a a^2*X+a a*X+1  1 a^2*X  1 a*X+a^2  1  X  1  1 X+a^2  X  1 X+a^2  1  1 X+a^2  0  a a^2*X+a^2 X+1  a  1  a a*X+a  X a^2 a*X+a  X  1  1  1  1  1 a*X+a a^2*X+a  1 X+a^2 a^2*X+a^2 a*X+1 a*X+1  a  1 a^2*X a^2*X+a a*X+a a*X a^2*X  X a^2*X+1  1  1 a^2*X+a X+a^2 X+1 a*X+a  1 a*X  X  0
 0  0 a^2*X  0  0  0  X  X  X  X  X  X a^2*X a^2*X a*X  X a*X a^2*X a^2*X  0 a^2*X a^2*X a*X  X  0 a*X  0 a*X  X  0 a^2*X a*X a^2*X a^2*X  X a*X a^2*X  X a*X a*X a^2*X a^2*X a*X a^2*X a*X a*X a^2*X a*X  X  X  X a*X a^2*X  0 a*X a^2*X a*X a*X a^2*X  0  X a^2*X a^2*X  X a*X a^2*X a^2*X a^2*X a^2*X a^2*X  0 a*X a^2*X  0 a^2*X a*X  0  X a*X  0 a^2*X a^2*X  X  0  0 a^2*X  0 a*X  0 a^2*X a*X a*X  0  X a*X  0  0  X  0
 0  0  0  X  0  X a^2*X  0  X a^2*X  X  0 a*X a^2*X  0 a^2*X  0  0 a*X a*X  X  X a^2*X  0  X  0 a*X a^2*X a^2*X  0  X a*X  0  X  0 a^2*X a*X a*X  X a^2*X  0  0  X a^2*X a*X  0 a^2*X  X  0 a*X a^2*X a^2*X  X a^2*X a*X a^2*X a^2*X  0 a*X  X a*X  X  X a*X a*X a*X  0 a*X  0 a*X  0  X  X a*X a^2*X  0 a*X a^2*X a^2*X a^2*X a^2*X a*X a^2*X a^2*X a*X a*X a^2*X  0  0  X  0  X  X  0 a^2*X  X  0  X  0
 0  0  0  0 a^2*X a^2*X  X a^2*X a*X  0 a^2*X  X  X a*X  X a*X a*X  X a^2*X a^2*X  0 a^2*X a^2*X a*X a*X a^2*X  0 a^2*X a^2*X a*X a*X  0 a^2*X  X a^2*X  X  X  X  0 a*X a^2*X a*X a*X  0  X  X  X  X a*X a^2*X a^2*X a*X  X a*X a^2*X a*X  0  0 a^2*X  0  X  X  0  0  0  X  0  0  0  0 a*X a^2*X  0 a*X a^2*X  0 a*X a^2*X  0  X  X a*X  0 a^2*X a^2*X a*X a^2*X a*X  X  X  X a^2*X  X  0 a^2*X  X a^2*X a^2*X  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+63x^280+48x^281+60x^282+456x^283+195x^284+336x^285+288x^286+1284x^287+150x^288+384x^289+576x^290+1404x^291+162x^292+480x^293+396x^294+1428x^295+99x^296+468x^297+636x^298+1584x^299+60x^300+576x^301+504x^302+1500x^303+63x^304+504x^305+456x^306+972x^307+48x^308+240x^309+156x^310+492x^311+21x^312+36x^313+96x^315+33x^316+45x^320+15x^324+33x^328+6x^332+9x^336+9x^340+3x^344+6x^352+3x^360

The gray image is a linear code over GF(4) with n=396, k=7 and d=280.
This code was found by Heurico 1.16 in 2.42 seconds.