The generator matrix

 1  0  1  1  1  1  1  1  1  0  1  1  1  0  1  1  X  1  1  1  1  1  1  1  X  1  1  1  1  1 aX  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X (a+1)X aX  X (a+1)X  X  X aX aX  1  1  1  1  1  1  1  1  0  X aX aX  1  1  1  1  1  1  1  1
 0  1  1  a (a+1)X+a+1  0 (a+1)X+1  a (a+1)X+a+1  1  0  a (a+1)X+1  1 (a+1)X+a+1 X+a  1  X (a+1)X+1 aX+a+1 X+a  X  1 aX+a+1  1  X aX+1 a+1  0 X+a  1 aX+1  a aX+a+1  X (a+1)X+a aX+a+1 aX (a+1)X+a+1 a+1  a a+1 a+1  X aX+a+1 (a+1)X+a aX X+a+1 (a+1)X+1 aX+a  1 (a+1)X+a+1 (a+1)X+a X+a X+a (a+1)X+a (a+1)X+a a+1 aX+1 aX+1 aX+1 X+1 (a+1)X+1  1  1  1  0  1  1  1  1  1  1  1  1  1 aX aX  0  X (a+1)X  0 aX  X  1  1  1  1 aX aX aX (a+1)X  0 (a+1)X+1  a (a+1)X+a+1
 0  0 (a+1)X  0  X  X (a+1)X  X (a+1)X  X  0  0  X  X  0 (a+1)X aX aX  0 (a+1)X aX (a+1)X aX aX (a+1)X  X  X  0 (a+1)X  X (a+1)X (a+1)X  X  0  X  0 (a+1)X  0 (a+1)X  X (a+1)X  X aX aX aX aX (a+1)X  0  0 (a+1)X aX  X (a+1)X aX  X aX  0 aX aX aX  X (a+1)X  X aX  0  0 aX (a+1)X aX  0  X  0 (a+1)X aX  0  X  0  X  0  X (a+1)X aX  X aX  0  X aX (a+1)X  X  0 aX  X aX  X aX aX
 0  0  0  X aX  X aX (a+1)X (a+1)X  0  X (a+1)X  0 aX aX (a+1)X  0  X  0 aX (a+1)X  X  0 aX  0  0 aX (a+1)X  0  X aX (a+1)X aX  X (a+1)X aX  X (a+1)X  0  0 aX  X  X (a+1)X  0 aX (a+1)X  0 aX  X aX (a+1)X  0  0  0  X  0 (a+1)X aX  X (a+1)X  X  X (a+1)X (a+1)X  X  0  X  X aX  X  X (a+1)X (a+1)X (a+1)X (a+1)X  0  0 aX  X aX  X aX aX  X (a+1)X (a+1)X  X  X aX  0 aX aX aX  0 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+192x^280+636x^281+291x^284+1548x^285+252x^288+96x^289+96x^292+84x^293+18x^296+216x^297+108x^300+432x^301+57x^304+60x^305+9x^316

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 0.41 seconds.