The generator matrix

 1  0  1  1  1 X^2+X  1  1  0  1  X X^2  1  1  1  1  1  1  1  X  X  X
 0  1  1  0 X^2+X+1  1  X X+1  1  0  1  1 X+1 X^2+X+1  1 X^2+1 X^2+X X+1  0 X^2+X X^2+X  1
 0  0  X  0 X^2+X X^2  0  0  X  X  0  X  X X^2 X^2+X X^2+X  0 X^2  X  X  X  X
 0  0  0  X  0 X^2 X^2+X  0  X X^2+X X^2+X X^2  0 X^2+X  X X^2+X X^2 X^2  X X^2+X X^2  0
 0  0  0  0 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2  0 X^2  0  0  0 X^2  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+179x^18+124x^19+292x^20+264x^21+363x^22+256x^23+293x^24+120x^25+94x^26+4x^27+54x^28+3x^30+1x^34

The gray image is a linear code over GF(2) with n=88, k=11 and d=36.
This code was found by Heurico 1.16 in 0.959 seconds.