The generator matrix

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

generates a code of length 22 over Z2[X]/(X^3) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+126x^16+56x^17+511x^18+412x^19+1081x^20+1060x^21+1624x^22+1080x^23+1229x^24+416x^25+405x^26+44x^27+123x^28+4x^29+19x^30+1x^38

The gray image is a linear code over GF(2) with n=88, k=13 and d=32.
This code was found by Heurico 1.16 in 0.792 seconds.