The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X X^2  X  X X^2
 0  X  0  0  0  0  0  0 X^2+X X^2+X  X  X  X  X  0  X X^2  X  X X^2  X  X
 0  0  X  0  0  0  X X^2+X  X  X X^2  X  X  0 X^2+X X^2 X^2  X  X  0 X^2+X  X
 0  0  0  X  0  X  X  X X^2  X X^2+X  X X^2 X^2 X^2 X^2+X  X  0  X X^2+X X^2  X
 0  0  0  0  X  X  0  X  X  0  X  X  0 X^2+X X^2+X  0  X X^2  X  X X^2  X
 0  0  0  0  0 X^2  0  0  0  0  0  0 X^2  0 X^2 X^2  0 X^2 X^2  0 X^2 X^2
 0  0  0  0  0  0 X^2  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  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+514x^16+256x^18+2496x^20+1536x^22+2712x^24+256x^26+384x^28+37x^32

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 14.2 seconds.