The generator matrix

 1  0  0  0  1  1  1  0  1  1  1  1  X  X  1  X  1  1
 0  1  0  0  0  1  1  1  X  X X+1  0  0  1  1  1  X  X
 0  0  1  0  1  1  0  1  0  1  1 X+1  1  0 X+1  0  X  1
 0  0  0  1  1  0  1  1  1  0  1  0  1  1  X  X  X  X
 0  0  0  0  X  0  0  0  0  X  0  X  X  0  X  X  X  0
 0  0  0  0  0  X  0  0  0  X  X  X  0  X  0  X  0  X
 0  0  0  0  0  0  X  0  0  0  X  X  X  X  0  X  X  0
 0  0  0  0  0  0  0  X  X  0  X  X  X  0  0  0  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+28x^11+136x^12+136x^13+160x^14+328x^15+622x^16+520x^17+192x^18+544x^19+656x^20+344x^21+160x^22+120x^23+112x^24+24x^25+4x^27+8x^28+1x^32

The gray image is a linear code over GF(2) with n=36, k=12 and d=11.
This code was found by Heurico 1.16 in 0.244 seconds.