The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  X  X X^2  0  X  1  X  1  X  0  1
 0  X  0  X  0  0  X X^2+X  0 X^2  X X^2  X  X  0 X^2+X  0 X^2  0  X  X  0
 0  0  X  X  0 X^2+X  X  0 X^2  X  X  X  X X^2+X  X  0  0  X X^2+X  X X^2 X^2
 0  0  0 X^2  0  0  0 X^2 X^2 X^2  0 X^2  0  0  0 X^2 X^2  0 X^2  0  0 X^2
 0  0  0  0 X^2  0  0  0  0  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2  0  0
 0  0  0  0  0 X^2  0  0  0 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2  0
 0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2  0  0  0  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+34x^16+56x^17+112x^18+160x^19+229x^20+296x^21+284x^22+304x^23+220x^24+152x^25+104x^26+48x^27+26x^28+8x^29+12x^30+1x^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 0.0654 seconds.