The generator matrix

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

generates a code of length 17 over Z2[X]/(X^2) who´s minimum homogenous weight is 10.

Homogenous weight enumerator: w(x)=1x^0+99x^10+158x^11+296x^12+404x^13+668x^14+836x^15+965x^16+1252x^17+1002x^18+928x^19+700x^20+380x^21+268x^22+124x^23+82x^24+12x^25+11x^26+2x^27+4x^28

The gray image is a linear code over GF(2) with n=34, k=13 and d=10.
As d=10 is an upper bound for linear (34,13,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 13.
This code was found by Heurico 1.16 in 0.842 seconds.