The generator matrix

 1  1  1  1  1  1  1  1  1  1  X  X  1  0  X  0  X  1
 0  X  0  0  0  X X^2+X  X X^2 X^2 X^2  0 X^2  X  X  X X^2+X  X
 0  0  X  0  X  X  X  0 X^2  0  X  X X^2 X^2+X X^2 X^2+X X^2+X X^2+X
 0  0  0  X  X  0  X X^2+X  0  X X^2  X X^2+X  X  X  X  X  X
 0  0  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0
 0  0  0  0  0 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2  0  0  0 X^2

generates a code of length 18 over Z2[X]/(X^3) who´s minimum homogenous weight is 13.

Homogenous weight enumerator: w(x)=1x^0+60x^13+96x^14+154x^15+247x^16+304x^17+352x^18+270x^19+238x^20+204x^21+64x^22+22x^23+24x^24+8x^25+2x^27+2x^28

The gray image is a linear code over GF(2) with n=72, k=11 and d=26.
This code was found by Heurico 1.16 in 3.17 seconds.