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

generates a code of length 53 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 156.

Homogenous weight enumerator: w(x)=1x^0+462x^156+438x^160+18x^164+96x^168+9x^176

The gray image is a linear code over GF(4) with n=212, k=5 and d=156.
This code was found by Heurico 1.16 in 0.031 seconds.