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

generates a code of length 52 over F4[X,sigma]/(X^2) who�s minimum homogenous weight is 148.

Homogenous weight enumerator: w(x)=1x^0+24x^148+96x^152+825x^156+33x^160+30x^164+9x^172+3x^176+3x^208

The gray image is a linear code over GF(4) with n=208, k=5 and d=148.
This code was found by Heurico 1.16 in 0.031 seconds.