The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  X  1  0  X  1 X^2  1  X  1  1
 0  X  0  0  0  0  0 X^2 X^2  X X^2+X X^2+X X^2  X  X X^2  0  X  0  X  0  0
 0  0  X  0  0 X^2 X^2+X  X  X  X  X X^2+X  0  0  X X^2  X X^2  X X^2+X  X  0
 0  0  0  X  0 X^2+X X^2+X  X X^2 X^2+X X^2+X X^2+X X^2+X X^2+X X^2+X X^2+X X^2 X^2+X X^2  0 X^2  0
 0  0  0  0  X  X X^2 X^2+X  X X^2+X X^2  0  X X^2  0 X^2  X X^2  0 X^2 X^2+X  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+43x^16+68x^17+81x^18+130x^19+224x^20+308x^21+332x^22+318x^23+218x^24+156x^25+86x^26+30x^27+24x^28+12x^29+12x^30+2x^31+2x^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 0.0664 seconds.