The generator matrix

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

generates a code of length 64 over Z2[X]/(X^3) who´s minimum homogenous weight is 62.

Homogenous weight enumerator: w(x)=1x^0+288x^62+59x^64+96x^66+64x^70+4x^80

The gray image is a linear code over GF(2) with n=256, k=9 and d=124.
This code was found by Heurico 1.16 in 35.7 seconds.