The generator matrix

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

generates a code of length 18 over Z2[X]/(X^2) who´s minimum homogenous weight is 10.

Homogenous weight enumerator: w(x)=1x^0+40x^10+64x^11+188x^12+256x^13+468x^14+648x^15+834x^16+1072x^17+1028x^18+1080x^19+844x^20+672x^21+476x^22+248x^23+172x^24+48x^25+36x^26+8x^27+8x^28+1x^32

The gray image is a linear code over GF(2) with n=36, k=13 and d=10.
This code was found by Heurico 1.16 in 0.648 seconds.