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

generates a code of length 97 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 284.

Homogenous weight enumerator: w(x)=1x^0+72x^284+264x^288+612x^292+36x^296+24x^300+12x^316+3x^384

The gray image is a linear code over GF(4) with n=388, k=5 and d=284.
This code was found by Heurico 1.16 in 0.187 seconds.