The generator matrix

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

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+96x^10+178x^11+253x^12+418x^13+660x^14+850x^15+1065x^16+1170x^17+996x^18+902x^19+658x^20+438x^21+284x^22+118x^23+70x^24+22x^25+12x^26+1x^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 0.728 seconds.