The generator matrix

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

generates a code of length 18 over Z2[X]/(X^2) who´s minimum homogenous weight is 13.

Homogenous weight enumerator: w(x)=1x^0+56x^13+89x^14+84x^15+115x^16+116x^17+115x^18+120x^19+116x^20+80x^21+47x^22+52x^23+24x^24+4x^25+5x^26

The gray image is a linear code over GF(2) with n=36, k=10 and d=13.
This code was found by Heurico 1.10 in 0.031 seconds.