The generator matrix

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

generates a code of length 17 over Z2[X]/(X^2) who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+224x^12+256x^14+590x^16+384x^18+448x^20+128x^22+16x^24+1x^32

The gray image is a linear code over GF(2) with n=34, k=11 and d=12.
As d=12 is an upper bound for linear (34,11,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 11.
This code was found by Heurico 1.16 in 2.99 seconds.