The generator matrix

 1  0  1  1  1 X^2+X  1  1  0  1  1 X^2+X  1  1  1  1  1  1
 0  1 X+1 X^2+X  1  1  0 X+1  1 X^2+X X^2+1  1  0 X^2+X  0 X^2+X X+1 X^2+1
 0  0 X^2  0  0  0  0 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2  0  0
 0  0  0 X^2  0  0 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2  0  0 X^2
 0  0  0  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0  0
 0  0  0  0  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2 X^2  0  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+53x^14+32x^15+194x^16+96x^17+279x^18+96x^19+183x^20+32x^21+51x^22+5x^24+1x^26+1x^28

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 0.011 seconds.