The generator matrix

 1  0  0  1  1  1  1  1  1  1  1  1  1  1 a^2*X a^2*X  1  1  1  1  0  1  1  1  1 a^2*X  1 a^2*X  1  1  1  X  1  1 a^2*X a^2*X  1  1  1  1  1  1  X  1  1  1  1  1  0  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 0  1  0  0  0 a^2*X  1 a^2*X+a a^2 a^2*X+1 a^2*X+1  a a^2*X+a^2 a^2  1  1 a^2*X+a  1 a^2*X+a^2  a  1 a*X+a^2 a^2 a^2*X+1 a*X  1  a a*X X+1 a^2*X a^2*X+a  1  a X+a^2  1  1 a*X+1 a^2*X+a  0 X+a a*X X+a^2  1 X+a^2 X+1 a^2 a^2*X+1 a^2*X+a^2  1  X  0  1 a*X+1 a^2*X+1 X+1 X+a^2 a*X+a a^2*X+a  a a^2*X+a a^2  a a*X+a^2 a^2*X+1
 0  0  1  1  a a^2  1 X+1  1  a  0  X a*X+a a^2 X+1 a^2 X+a^2 a^2  0 a*X+a X+a X+1 a^2*X X+a^2  X a*X+a^2  0  1 X+a a*X+1 X+a^2  1 a^2*X+1 a^2 a^2*X+1  X a*X  0 a^2*X+a^2 a^2 a*X+a a^2*X+a  a  X  1 X+a^2  a X+a a^2*X+a  a a^2*X+1 X+a^2 a*X+a a^2*X+a^2 a^2*X a*X a*X+1 a*X+a^2 a^2*X a*X+a X+a X+a^2 a*X+a  0
 0  0  0 a^2*X  0  0  0  X  X  X a^2*X a*X a*X a*X a*X a^2*X a^2*X  X a^2*X  X a*X  0  0 a*X a^2*X a*X a*X  X a^2*X a*X  0 a*X  X  0  0 a^2*X  0  0  X  X a^2*X  X  0 a*X  X  X  0  X  X a*X a*X  0  X  X a*X  0 a^2*X  X a*X a*X a*X a^2*X  0 a^2*X
 0  0  0  0  X a^2*X a*X  X a^2*X a*X a*X  X  0 a*X  X a*X  X a^2*X  X a*X  0  X a*X  0 a^2*X a^2*X  0 a^2*X  0 a*X  0 a^2*X  0 a*X  X  0 a^2*X a*X a*X  X  X  0  X a*X  0 a*X  0  X a*X a^2*X  X a^2*X  X  0 a^2*X  0 a^2*X a^2*X a*X  0 a^2*X a*X a^2*X a^2*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+1044x^176+4482x^180+7944x^184+11352x^188+14055x^192+13398x^196+9183x^200+3408x^204+537x^208+69x^212+33x^216+21x^220+3x^224+3x^228+3x^236

The gray image is a linear code over GF(4) with n=256, k=8 and d=176.
This code was found by Heurico 1.16 in 51.4 seconds.