The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 0 X^2  0  0  0 X^2  0  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0
 0  0 X^2  0  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0  0
 0  0  0 X^2  0 X^2 X^2 X^2  0  0 X^2  0  0 X^2 X^2 X^2  0
 0  0  0  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0  0 X^2  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+15x^16+96x^17+15x^18+1x^34

The gray image is a linear code over GF(2) with n=68, k=7 and d=32.
As d=32 is an upper bound for linear (68,7,2)-codes, this code is optimal over Z2[X]/(X^3) for dimension 7.
This code was found by Heurico 1.16 in 0.00139 seconds.