The generator matrix

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

generates a code of length 18 over Z2[X]/(X^3) who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+85x^8+112x^10+544x^12+64x^13+572x^14+1088x^15+587x^16+4992x^17+336x^18+4992x^19+440x^20+1088x^21+776x^22+64x^23+383x^24+224x^26+8x^28+28x^30

The gray image is a linear code over GF(2) with n=72, k=14 and d=16.
This code was found by Heurico 1.16 in 0.457 seconds.