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

generates a code of length 96 over F4[X]/(X^2) who´s minimum homogenous weight is 280.

Homogenous weight enumerator: w(x)=1x^0+177x^280+276x^281+384x^282+555x^284+696x^285+360x^286+303x^288+240x^289+168x^290+120x^292+108x^293+108x^294+90x^296+72x^297+48x^298+69x^300+48x^301+24x^302+39x^304+24x^305+24x^306+24x^308+60x^309+36x^310+27x^312+12x^313+3x^336

The gray image is a linear code over GF(4) with n=384, k=6 and d=280.
This code was found by Heurico 1.16 in 0.219 seconds.