The generator matrix

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

generates a code of length 22 over Z2[X]/(X^3) who´s minimum homogenous weight is 18.

Homogenous weight enumerator: w(x)=1x^0+71x^18+109x^20+158x^22+105x^24+56x^26+7x^28+2x^30+2x^32+1x^34

The gray image is a linear code over GF(2) with n=88, k=9 and d=36.
This code was found by Heurico 1.16 in 0.0183 seconds.