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 a*X  0  X a^2*X a*X a^2*X a*X  X  X a*X  0 a^2*X a*X  X a*X  0  X  0 a^2*X a*X  X a^2*X a*X  0 a*X  0 a*X  X a*X  X a*X  X  0  0  0  0 a^2*X a*X a*X a*X  X  X a*X  X a^2*X  0 a*X  X a^2*X  0  X  0 a*X a^2*X
 0  0  X  0  0  X a^2*X a*X a*X a*X  0  0 a*X a*X  0 a*X a^2*X a*X a^2*X a^2*X  0  X a^2*X  0 a^2*X  0 a*X a*X a*X a*X a^2*X  0 a^2*X  0 a^2*X  0  X a*X a^2*X a^2*X  X  X a^2*X a^2*X  0  0  X a^2*X a^2*X  X  0 a*X  0  X a*X  X a*X a^2*X  0 a*X  X  X a*X
 0  0  0  X  0 a^2*X  0  X a*X a^2*X  X  X  X  0  X a^2*X  X  X a^2*X a^2*X a^2*X a*X  0 a^2*X a^2*X  0  X a*X  0 a^2*X  0 a*X  X a*X  X  0  X a*X a*X  0  X a*X a*X a*X a^2*X a^2*X a*X a^2*X  0 a^2*X a*X a^2*X  0  X  0  0 a^2*X  0  X  X a^2*X a*X a*X
 0  0  0  0  X  X  X a^2*X  X  X  X a*X  0  0  0 a*X  X a*X a^2*X a^2*X a*X  0 a*X  X a*X a*X  0  0 a^2*X a^2*X a^2*X a*X  X  0  0  X  X a^2*X a*X  X a^2*X  X  0 a*X  X  0 a^2*X  0 a^2*X a^2*X  X  0  0  X a*X a^2*X  0 a*X a^2*X  X  X a*X a^2*X

generates a code of length 63 over F4[X]/(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 11.5 seconds.