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

generates a code of length 63 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 176.

Homogenous weight enumerator: w(x)=1x^0+189x^176+171x^180+192x^183+198x^184+1152x^187+66x^188+1728x^191+117x^192+66x^196+60x^200+27x^204+36x^208+36x^212+27x^216+12x^220+9x^224+3x^232+3x^236+3x^244

The gray image is a linear code over GF(4) with n=252, k=6 and d=176.
This code was found by Heurico 1.16 in 11.7 seconds.