The generator matrix

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

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+49x^16+104x^17+194x^18+328x^19+438x^20+600x^21+666x^22+592x^23+492x^24+312x^25+150x^26+104x^27+42x^28+8x^29+14x^30+2x^32

The gray image is a linear code over GF(2) with n=88, k=12 and d=32.
This code was found by Heurico 1.16 in 0.177 seconds.