The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^2  1  1  1 X^2+X  0  1  1 X^2  1
 0  1  1 X^2+X X^2+X+1  1 X^2 X+1  1  X X^2+1  0  1  1 X^2+X+1 X^2  1 X+1
 0  0  X  0 X^2+X  0  X X^2 X^2+X  X  0  0 X^2 X^2  X X^2+X X^2+X  0
 0  0  0 X^2  0  0  0 X^2  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2 X^2
 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 X^2
 0  0  0  0  0 X^2 X^2  0  0 X^2  0  0 X^2  0 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+117x^14+64x^15+385x^16+192x^17+552x^18+192x^19+360x^20+64x^21+98x^22+22x^24+1x^30

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 0.0833 seconds.