The generator matrix

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

generates a code of length 18 over Z2[X]/(X^2) who´s minimum homogenous weight is 11.

Homogenous weight enumerator: w(x)=1x^0+96x^11+226x^12+296x^13+400x^14+600x^15+902x^16+1032x^17+1008x^18+1080x^19+972x^20+632x^21+368x^22+264x^23+200x^24+88x^25+16x^26+8x^27+2x^28+1x^32

The gray image is a linear code over GF(2) with n=36, k=13 and d=11.
This code was found by Heurico 1.10 in 5.55 seconds.