The generator matrix

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

generates a code of length 64 over Z2[X]/(X^4) who´s minimum homogenous weight is 62.

Homogenous weight enumerator: w(x)=1x^0+264x^62+96x^63+301x^64+96x^65+264x^66+2x^96

The gray image is a linear code over GF(2) with n=512, k=10 and d=248.
This code was found by Heurico 1.16 in 1.28 seconds.