The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  X
 0 X^2  0  0  0  0  0  0  0  0  0  0  0  0 X^2  0 X^2 X^2
 0  0 X^2  0  0  0  0  0  0  0  0  0  0  0 X^2 X^2  0 X^2
 0  0  0 X^2  0  0  0  0  0  0  0  0  0 X^2  0 X^2 X^2  0
 0  0  0  0 X^2  0  0  0  0  0  0  0  0 X^2  0  0 X^2 X^2
 0  0  0  0  0 X^2  0  0  0  0  0  0  0 X^2  0 X^2  0 X^2
 0  0  0  0  0  0 X^2  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0
 0  0  0  0  0  0  0 X^2  0  0  0  0 X^2  0  0  0 X^2 X^2
 0  0  0  0  0  0  0  0 X^2  0  0  0 X^2  0  0 X^2 X^2  0
 0  0  0  0  0  0  0  0  0 X^2  0  0 X^2  0  0 X^2  0 X^2
 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 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 8.

Homogenous weight enumerator: w(x)=1x^0+126x^8+532x^12+2404x^16+10240x^18+2392x^20+602x^24+84x^28+3x^32

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 0.812 seconds.