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

generates a code of length 56 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 160.

Homogenous weight enumerator: w(x)=1x^0+24x^160+66x^164+864x^168+39x^172+12x^176+12x^180+3x^188+3x^224

The gray image is a linear code over GF(4) with n=224, k=5 and d=160.
This code was found by Heurico 1.16 in 0.031 seconds.