The generator matrix

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

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+199x^14+336x^15+499x^16+632x^17+669x^18+824x^19+492x^20+232x^21+153x^22+24x^23+32x^24+3x^26

The gray image is a linear code over GF(2) with n=72, k=12 and d=28.
This code was found by Heurico 1.16 in 88.2 seconds.