The generator matrix

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

generates a code of length 22 over Z2[X]/(X^3) who´s minimum homogenous weight is 17.

Homogenous weight enumerator: w(x)=1x^0+74x^17+230x^18+256x^19+609x^20+396x^21+896x^22+546x^23+607x^24+186x^25+182x^26+60x^27+31x^28+16x^29+4x^30+2x^31

The gray image is a linear code over GF(2) with n=88, k=12 and d=34.
This code was found by Heurico 1.16 in 0.164 seconds.