The generator matrix

 1  0  1  1  1 X^2+X  1 X^2  1  1  X  1  0  1  1  1  1  1  1  0 X^2+X  X
 0  1  1 X^2+X X^2+X+1  1 X^2  1 X+1  X  1 X^2+1  1  X X^2 X^2+1 X^2  X X^2  1  1  0
 0  0  X  0 X^2+X X^2  X  X  0 X^2+X X^2+X  0 X^2  X  X X^2 X^2  0 X^2+X  X  0  0
 0  0  0 X^2  0 X^2  0 X^2 X^2 X^2  0  0 X^2  0 X^2  0 X^2  0  0  0 X^2 X^2
 0  0  0  0 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2  0 X^2  0  0  0  0 X^2  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+65x^18+72x^19+161x^20+120x^21+190x^22+120x^23+174x^24+72x^25+29x^26+13x^28+4x^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 0.0165 seconds.