The generator matrix

 1  0  1  1  1  X  1  1 X^2+X  1  1  X X^3+X^2+X X^2  1  1 X^3+X^2  1  1  1  1 X^2  1  1  1  0  1  1  1  1 X^3  1  X  1  1  0  1 X^2+X  1  0  1  1  1  1 X^2  X  1  1  X X^2+X  X  1 X^3+X^2+X X^2+X X^3+X^2 X^3  X X^2+X  1  0 X^3+X X^3+X  X  1
 0  1  1 X^2 X+1  1  X X^3+1  1 X^2+X X^3+X+1  1  1  1  0 X^3+X^2+X+1  1 X^3+X^2 X^2+X+1 X^3+X^2+X X^2+1  1 X^3+X^2+1 X^3 X^3+X^2  1 X^3+X  X X^3+X^2+X+1 X^2+X  1 X^2+1  1 X^3+X+1 X^2+X+1  1 X^2+X  1  0 X^3+X^2 X^3+X^2+1 X^2  X X^3+X+1  1  1 X^3+1 X^3+1 X^3  1 X^3+X^2+X  0  1  1  X  1  1  1  X  1  1  1 X^3 X^2
 0  0  X X^3+X X^3 X^3+X X^3+X X^3  0  0  X X^2+X X^3+X^2 X^2 X^3+X^2 X^3+X^2+X X^2+X X^2+X X^2 X^3+X X^2+X X^3+X X^3+X^2  X X^3 X^3+X^2  0 X^2+X X^3 X^2  X  0 X^3+X^2 X^3+X^2+X X^3+X X^2+X X^3+X^2+X X^3+X X^2+X  X  X X^3+X^2 X^3+X^2 X^3+X^2 X^3  0 X^3+X^2+X X^3+X^2  X  X X^3+X^2+X X^3+X X^2+X X^3+X^2+X X^2 X^2+X  X X^3  X X^2  0 X^2 X^3  0

generates a code of length 64 over Z2[X]/(X^4) who´s minimum homogenous weight is 61.

Homogenous weight enumerator: w(x)=1x^0+326x^61+348x^62+404x^63+146x^64+280x^65+216x^66+160x^67+24x^68+94x^69+27x^70+8x^71+4x^72+4x^75+4x^77+1x^80+1x^86

The gray image is a linear code over GF(2) with n=512, k=11 and d=244.
This code was found by Heurico 1.16 in 0.391 seconds.