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  1  1  X  1  1  1  X  1  1  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 a*X  0  X  0 a*X  X a*X a*X a*X a*X  X  0  0  X a*X  0  0  X a^2*X a*X  X  0 a*X  0  X a^2*X a*X  0  X  0
 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  X  0 a*X a^2*X a^2*X  X  0 a*X  0 a*X  X  0 a*X a^2*X  X  X  0 a*X a*X a^2*X  0  X  X a^2*X  X  0 a^2*X  0 a^2*X  X  0
 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  0 a*X  X a*X  0 a*X a*X a*X  X  X  X a*X a*X  0 a*X  X a*X  0 a*X a*X  0  0  X a*X  X a*X a*X  0 a*X  X  0
 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 a*X  0 a*X a*X a*X a^2*X a^2*X a^2*X  0  X  X  X  0 a^2*X a^2*X  0 a*X a*X a^2*X a*X  0 a*X a^2*X  X  0  X a^2*X a*X a*X  X a*X

generates a code of length 64 over F4[X]/(X^2) who´s minimum homogenous weight is 176.

Homogenous weight enumerator: w(x)=1x^0+48x^176+153x^180+225x^184+192x^186+135x^188+1152x^190+108x^192+1728x^194+75x^196+75x^200+51x^204+45x^208+33x^212+21x^216+27x^220+18x^224+3x^228+3x^236+3x^248

The gray image is a linear code over GF(4) with n=256, k=6 and d=176.
This code was found by Heurico 1.16 in 0.215 seconds.