The generator matrix

 1  0  0  1  1  1  1  1  1  1  1  1  1  X  1 aX  1  1  1  1 (a+1)X  1  1  1  1  1  1  1  1  1  1  1  0 aX (a+1)X  1  1  1  X  1  X  1  1  1  1  1  1 aX  1  1  1  1  X (a+1)X  1  1  1  1  1  1  1  0  1  1  1 (a+1)X  1  1  X aX  1  1  0  1  1 aX  1  0  1  1  1  1 (a+1)X  0  1  1  1 aX  1  1  1  X  1  1  1  1
 0  1  0 (a+1)X  X aX  1 (a+1)X+a a+1 (a+1)X+1 X+1 aX+1 X+a+1  1  a  1 (a+1)X+a X+a (a+1)X+a+1 aX+a+1  1  0 aX+a (a+1)X+1 X+a X+a+1 (a+1)X+a+1 aX+a+1 aX+a X+1 (a+1)X a+1  1  0  1  X X+a+1  1  1 aX+1  1 (a+1)X+a+1 X+a  a (a+1)X+1 a+1 (a+1)X+a+1  1 a+1 (a+1)X+a+1  a  1  1  1 X+a+1 aX+1  1 (a+1)X+1 aX+1 aX+a+1 (a+1)X+1  1 aX+a (a+1)X+a X+a  1 aX+a+1 (a+1)X+a  1  1 X+a+1 aX+1  1 (a+1)X  X  1 aX aX aX+a X+a+1 X+a  a  1  1  0 (a+1)X  a  1 a+1  a  1  1  X a+1 a+1 aX+a
 0  0  1  1 (a+1)X+a (a+1)X+a+1 a+1 aX+a+1 X+a+1 X+a X+1 (a+1)X aX+a X+a+1  a (a+1)X+1 aX aX+1  0 X+1  a  X  1 aX+a  X (a+1)X+1 X+a+1 (a+1)X X+a  X (a+1)X+1  a aX+a+1  1  1 X+a (a+1)X aX+a X+a  1 (a+1)X aX aX+a+1 aX+1 a+1 X+1  a X+a+1 (a+1)X+1 (a+1)X+a  X (a+1)X (a+1)X+a X+1 aX (a+1)X+a  X  1 aX  0 (a+1)X+1 (a+1)X+1 aX+a  a X+1 aX+a (a+1)X+a X+a aX+a+1 a+1  1 X+a X+1  X aX+1 (a+1)X+a X+a  1 X+1  a (a+1)X aX X+a (a+1)X+a+1 aX+a  0 aX+a aX+a+1 X+a  0  a  1  1 aX+1 aX aX

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

Homogenous weight enumerator: w(x)=1x^0+195x^280+492x^281+192x^282+72x^283+459x^284+672x^285+180x^286+72x^287+240x^288+444x^289+84x^290+24x^291+99x^292+180x^293+60x^294+66x^296+156x^297+12x^298+12x^299+63x^300+72x^301+24x^302+15x^304+60x^305+12x^307+60x^308+36x^309+24x^310+12x^312+3x^320+3x^348

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 0.25 seconds.