The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+4x^17+6x^18+4x^19+1x^20

The gray image is a linear code over GF(2) with n=34, k=4 and d=17.
As d=17 is an upper bound for linear (34,4,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 4.
This code was found by Heurico 1.16 in 0.000566 seconds.