The generator matrix

 1  0  1  1  1 X^2+X  1  1  0  1  1 X^2+X  1  1  1  1  1  1  1  1 X^2+X  X
 0  1 X+1 X^2+X  1  1  0 X+1  1 X^2+X X^2+1  1  0 X^2 X^2+X  0 X+1  0 X^2  0  1 X^2+X
 0  0 X^2  0  0  0  0 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2  0 X^2 X^2 X^2
 0  0  0 X^2  0  0 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2  0  0  0 X^2 X^2  0  0
 0  0  0  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0  0 X^2  0  0
 0  0  0  0  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2 X^2  0  0 X^2  0  0  0  0 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+74x^18+48x^19+161x^20+144x^21+186x^22+144x^23+145x^24+48x^25+54x^26+11x^28+6x^30+2x^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 1.26 seconds.