The generator matrix

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

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+97x^18+48x^19+197x^20+80x^21+218x^22+80x^23+158x^24+48x^25+61x^26+25x^28+8x^30+3x^32

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 0.0258 seconds.