The generator matrix

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

generates a code of length 17 over Z2[X]/(X^3) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+7x^16+46x^17+8x^18+2x^25

The gray image is a linear code over GF(2) with n=68, k=6 and d=32.
As d=32 is an upper bound for linear (68,6,2)-codes, this code is optimal over Z2[X]/(X^3) for dimension 6.
This code was found by Heurico 1.16 in 0.00106 seconds.