The generator matrix

 1  0  0  0  0  0  1  1  1  X  1  1  0  1  1  X  0  1
 0  1  0  0  0  0  0  0  0  0 X+1 X+1  1  X  X  X  1 X+1
 0  0  1  0  0  0  0 X+1  X  1  1  X X+1  0  X  1  X  1
 0  0  0  1  0  0  0  1 X+1  1  0  0  X  1  1  0 X+1  X
 0  0  0  0  1  0  1  0  1  1  1 X+1  X  1  0 X+1 X+1  1
 0  0  0  0  0  1  1 X+1  0 X+1  X  X  X  1  X  1 X+1 X+1
 0  0  0  0  0  0  X  X  X  X  0  X  X  0  0  0  0  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+90x^11+230x^12+298x^13+401x^14+624x^15+885x^16+1024x^17+1004x^18+1044x^19+1000x^20+644x^21+374x^22+288x^23+178x^24+80x^25+12x^26+2x^27+10x^28+2x^29+1x^30

The gray image is a linear code over GF(2) with n=36, k=13 and d=11.
This code was found by Heurico 1.16 in 1.68 seconds.