The generator matrix

1 0 0 0 0 0 1 1 1 1 0 X 1 1 0 1 1
0 1 0 0 0 0 0 0 1 1 1 X X X X 0 1
0 0 1 0 0 0 0 1 0 X 0 1 X+1 1 X X+1 0
0 0 0 1 0 0 0 1 1 0 X+1 X+1 0 X 1 X 0
0 0 0 0 1 0 1 0 X+1 X 1 0 X X+1 X+1 0 0
0 0 0 0 0 1 1 X+1 X X+1 X+1 0 1 X+1 1 0 1
0 0 0 0 0 0 X X 0 X X 0 0 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+94x^10+156x^11+316x^12+414x^13+636x^14+826x^15+985x^16+1238x^17+1016x^18+954x^19+664x^20+378x^21+292x^22+110x^23+78x^24+18x^25+10x^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 1.10 in 0.281 seconds.