The generator matrix

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

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+51x^12+80x^13+102x^14+112x^15+99x^16+130x^17+108x^18+120x^19+103x^20+60x^21+43x^22+8x^23+2x^24+2x^25+2x^26+1x^30

The gray image is a linear code over GF(2) with n=34, k=10 and d=12.
As d=12 is an upper bound for linear (34,10,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 10.
This code was found by Heurico 1.16 in 0.02 seconds.