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

generates a code of length 57 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 168.

Homogenous weight enumerator: w(x)=1x^0+336x^168+288x^170+180x^172+96x^174+54x^176+60x^180+9x^192

The gray image is a linear code over GF(4) with n=228, k=5 and d=168.
This code was found by Heurico 1.16 in 0.094 seconds.