The generator matrix

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

generates a code of length 18 over Z2[X]/(X^3) who´s minimum homogenous weight is 14.

Homogenous weight enumerator: w(x)=1x^0+36x^14+96x^15+126x^16+166x^17+200x^18+164x^19+106x^20+72x^21+33x^22+12x^23+7x^24+2x^25+2x^26+1x^30

The gray image is a linear code over GF(2) with n=72, k=10 and d=28.
This code was found by Heurico 1.16 in 0.0113 seconds.