The generator matrix

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

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+174x^14+199x^16+96x^18+40x^20+2x^22

The gray image is a linear code over GF(2) with n=64, k=9 and d=28.
As d=28 is an upper bound for linear (64,9,2)-codes, this code is optimal over Z2[X]/(X^3) for dimension 9.
This code was found by Heurico 1.11 in -6.48e-008 seconds.