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

generates a code of length 63 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 168.

Homogenous weight enumerator: w(x)=1x^0+240x^168+351x^172+72x^175+444x^176+360x^179+411x^180+1680x^183+447x^184+3600x^187+390x^188+4392x^191+330x^192+2184x^195+360x^196+312x^200+288x^204+222x^208+162x^212+69x^216+51x^220+15x^224+3x^228

The gray image is a linear code over GF(4) with n=252, k=7 and d=168.
This code was found by Heurico 1.16 in 96.5 seconds.