The generator matrix

1 0 0 0 0 1 1 1 X 1 1 X 1 X 1 X 0
0 1 0 0 0 0 0 X X 1 1 1 X+1 0 X 1 1
0 0 1 0 0 1 X 1 1 0 X+1 X 0 1 X+1 X+1 X+1
0 0 0 1 0 1 X+1 0 1 X X+1 0 1 X 1 1 1
0 0 0 0 1 X 1 1 X+1 1 X+1 0 1 1 X+1 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+56x^12+82x^13+79x^14+122x^15+116x^16+118x^17+126x^18+108x^19+78x^20+70x^21+51x^22+10x^23+5x^24+2x^25

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 1.10 in 0.016 seconds.