The generator matrix

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

generates a code of length 16 over Z2[X]/(X^3) who´s minimum homogenous weight is 14.

Homogenous weight enumerator: w(x)=1x^0+83x^14+91x^16+76x^18+4x^20+1x^30

The gray image is a linear code over GF(2) with n=64, k=8 and d=28.
As d=29 is an upper bound for linear (64,8,2)-codes, this code is optimal over Z2[X]/(X^3) for dimension 8.
This code was found by Heurico 1.16 in 0.00163 seconds.