The generator matrix

 1  0  1  1  1 X^2+X  1  1  0  1  1  1 X^2+X  1  1  1  1  1  1  1  0  1
 0  1 X+1 X^2+X  1  1  0 X+1  1 X^2+X X^2+1 X^2+X  1  0 X+1  0 X^2+X X^2+1 X^2+X  0  X  0
 0  0 X^2  0  0  0  0  0  0 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2  0  0  0
 0  0  0 X^2  0  0  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0  0
 0  0  0  0 X^2  0  0  0 X^2  0 X^2  0 X^2 X^2  0 X^2  0  0 X^2 X^2  0  0
 0  0  0  0  0 X^2  0 X^2 X^2  0 X^2  0  0 X^2  0 X^2 X^2 X^2  0  0  0  0
 0  0  0  0  0  0 X^2 X^2  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0  0  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+40x^16+18x^17+67x^18+212x^19+102x^20+542x^21+106x^22+536x^23+86x^24+206x^25+68x^26+20x^27+26x^28+2x^29+14x^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 0.0454 seconds.