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

generates a code of length 77 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 230.

Homogenous weight enumerator: w(x)=1x^0+180x^230+33x^232+24x^236+3x^240+12x^246+3x^248

The gray image is a linear code over GF(4) with n=308, k=4 and d=230.
This code was found by Heurico 1.16 in 0.078 seconds.