The generator matrix

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

generates a code of length 56 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 164.

Homogenous weight enumerator: w(x)=1x^0+87x^164+192x^165+108x^166+309x^168+144x^169+72x^170+15x^172+12x^174+6x^176+48x^177+24x^180+6x^188

The gray image is a linear code over GF(4) with n=224, k=5 and d=164.
This code was found by Heurico 1.16 in 0.016 seconds.