The generator matrix

 1  0  0  1  1  1  0  1  X  1 X^2+X  1  1  X  1  X  1  1  1  X  1  1
 0  1  0  0  1  1  1 X+1 X^2+X X^2+X  1 X+1  X  1  1  1 X+1 X^2+X+1 X^2+X+1  1 X^2  0
 0  0  1  1  0 X+1  1 X^2  1  1  X X^2+X+1 X^2 X^2+X+1  0 X^2+X  0 X+1  X X+1  X X^2+X
 0  0  0  X X^2 X^2+X  X X^2  X  0  X  0  X  0  X X^2+X X^2+X  X X^2  X X^2+X  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+84x^18+232x^19+305x^20+276x^21+288x^22+308x^23+237x^24+188x^25+88x^26+20x^27+15x^28+4x^30+2x^32

The gray image is a linear code over GF(2) with n=88, k=11 and d=36.
This code was found by Heurico 1.11 in 0.015 seconds.