The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  X  1  0  1  X  X  1  X  1 X^2
 0  X  0  X  0  0  X X^2+X X^2 X^2  X X^2+X  X X^2+X X^2  0 X^2+X  0  0 X^2+X  X  X
 0  0  X  X  0 X^2+X  X X^2  0  X  X X^2+X X^2+X X^2  X X^2  0 X^2+X  X  0 X^2  X
 0  0  0 X^2  0  0 X^2  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2
 0  0  0  0 X^2  0  0  0 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0
 0  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2  0 X^2  0  0  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+134x^18+199x^20+382x^22+174x^24+114x^26+8x^28+10x^30+1x^32+1x^36

The gray image is a linear code over GF(2) with n=88, k=10 and d=36.
This code was found by Heurico 1.16 in 56.6 seconds.