The generator matrix

 1  0  0  0  1  1  1 X^2+X  1  1  1 X^2+X  1  0  0  1  1  1  X  1  X  0
 0  1  0  0  0  1 X^2+X+1  1  X X+1  X  X X^2+1  1  1  X X^2+X+1 X+1  1  1  1  1
 0  0  1  0  1  1  X X+1  1 X^2+1  X  1  0 X+1  X X^2+X X+1  X X+1  1 X^2+X+1  X
 0  0  0  1  1  0 X^2  0 X^2 X^2+X+1 X^2+X+1 X+1 X+1 X+1 X^2+1  0 X^2+X  1 X^2+X X^2+1 X^2+X+1 X^2+1
 0  0  0  0  X  0  0 X^2 X^2 X^2+X X^2+X  X X^2 X^2 X^2 X^2+X X^2+X X^2  0  0 X^2+X X^2+X
 0  0  0  0  0 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2  0  0 X^2 X^2  0  0 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+268x^16+524x^17+1722x^18+2124x^19+4017x^20+4488x^21+6230x^22+4600x^23+4439x^24+2108x^25+1464x^26+444x^27+263x^28+48x^29+22x^30+4x^32+2x^34

The gray image is a linear code over GF(2) with n=88, k=15 and d=32.
This code was found by Heurico 1.16 in 8.71 seconds.