The generator matrix

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

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+36x^18+96x^19+150x^20+172x^21+148x^22+162x^23+134x^24+64x^25+36x^26+12x^27+2x^28+4x^29+4x^30+2x^31+1x^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 0.0159 seconds.