The generator matrix

 1  1  1  1  1  1  1  1  1  1  X  0  X  X  1  1  0  1  1  1  1  X
 0  X  0 X^2+X  0 X^2+X  0 X^2+X X^2 X^2+X X^2+X  X X^2+X X^2+X  0  0  X X^2+X X^2+X X^2+X  0 X^2+X
 0  0 X^2  0  0  0  0  0 X^2  0  0  0 X^2 X^2  0 X^2 X^2  0 X^2  0  0 X^2
 0  0  0 X^2  0  0  0  0  0  0 X^2 X^2 X^2 X^2  0  0  0  0  0 X^2 X^2 X^2
 0  0  0  0 X^2  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2
 0  0  0  0  0 X^2  0  0  0 X^2  0  0 X^2 X^2 X^2  0  0 X^2  0 X^2  0 X^2
 0  0  0  0  0  0 X^2  0 X^2  0  0 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2  0  0
 0  0  0  0  0  0  0 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2  0  0 X^2  0 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+83x^16+176x^18+485x^20+544x^22+514x^24+176x^26+58x^28+10x^32+1x^36

The gray image is a linear code over GF(2) with n=88, k=11 and d=32.
This code was found by Heurico 1.16 in 0.0695 seconds.