The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^2  1  1  X  1  1  X  0  X  X
 0  1  1  0 X^2+X+1  1  X X^2+X+1  1  1  0  1  0 X^2+1  1  X X^2 X^2+X
 0  0  X  0 X^2+X X^2  0  0 X^2+X X^2  0 X^2+X  X  0 X^2+X X^2 X^2+X  X
 0  0  0  X  0 X^2 X^2+X  X X^2 X^2+X X^2  0  X  0  X  X X^2 X^2+X
 0  0  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2  0 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+144x^14+140x^15+296x^16+224x^17+405x^18+296x^19+312x^20+96x^21+90x^22+12x^23+29x^24+1x^26+2x^28

The gray image is a linear code over GF(2) with n=72, k=11 and d=28.
This code was found by Heurico 1.16 in 1.38 seconds.