The generator matrix

 1  0  1  1  1  0  1  1  X  1  1  X  X  X  X  0  X
 0  1  1  0 X+1  1  X X+1  1  X  1  1  0  0  X  X  0
 0  0  X  0  X  0  0  X  0  0  X  0  X  X  X  X  0
 0  0  0  X  X  X  X  0  X  0  X  0  X  0  0  X  0

generates a code of length 17 over Z2[X]/(X^2) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+46x^16+16x^20+1x^32

The gray image is a linear code over GF(2) with n=34, k=6 and d=16.
As d=16 is an upper bound for linear (34,6,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 6.
This code was found by Heurico 1.16 in 0.000917 seconds.