The generator matrix

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

generates a code of length 99 over F4[X]/(X^2) who´s minimum homogenous weight is 290.

Homogenous weight enumerator: w(x)=1x^0+588x^290+552x^291+69x^292+732x^294+456x^295+123x^296+456x^298+240x^299+12x^300+192x^302+96x^303+15x^304+132x^306+48x^307+15x^308+84x^310+48x^311+6x^312+36x^314+24x^315+24x^318+72x^319+12x^320+60x^322+3x^328

The gray image is a linear code over GF(4) with n=396, k=6 and d=290.
This code was found by Heurico 1.16 in 0.281 seconds.