The generator matrix

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

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+80x^14+142x^16+256x^17+96x^18+256x^19+96x^20+80x^22+16x^24+1x^32

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 0.0244 seconds.