The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  X  1  X  1  1  X  1
 0  X  0  0  0  X X^2+X  X X^2 X^2  0  0  X  0  X X^2  X  X  X X^2+X  0  0
 0  0  X  0  X  X  X  0 X^2  0  X X^2+X X^2+X  0 X^2 X^2  X X^2+X  0  0  X  0
 0  0  0  X  X  0  X X^2+X  0  X  X X^2 X^2 X^2+X  X X^2+X X^2 X^2 X^2+X X^2+X  X  0
 0  0  0  0 X^2  0  0  0 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2  0 X^2  0
 0  0  0  0  0 X^2  0 X^2  0  0 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2  0  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+51x^16+56x^17+93x^18+100x^19+313x^20+92x^21+620x^22+120x^23+311x^24+96x^25+106x^26+36x^27+27x^28+12x^29+12x^30+1x^32+1x^34

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 0.066 seconds.