The generator matrix

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

generates a code of length 96 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 264.

Homogenous weight enumerator: w(x)=1x^0+216x^264+330x^268+378x^272+372x^276+240x^277+411x^280+960x^281+372x^284+3360x^285+339x^288+4800x^289+330x^292+2928x^293+255x^296+276x^300+222x^304+153x^308+123x^312+90x^316+90x^320+51x^324+39x^328+30x^332+6x^336+6x^340+3x^348+3x^364

The gray image is a linear code over GF(4) with n=384, k=7 and d=264.
This code was found by Heurico 1.16 in 4.91 seconds.