The generator matrix

 1  0  0  0  1  1  1 X^2+X  X  X  1  1  1  X  1  1  1  1  1  1  X  1
 0  1  0  0  0  1 X+1  1 X^2  1  X  1 X^2+1  1  0 X+1 X+1 X^2+X+1 X^2+X X^2+X  1 X^2
 0  0  1  0  0  1 X^2+X+1 X^2  1 X+1 X^2+X+1 X^2+X  0 X^2+X+1 X+1 X^2 X^2+X  X  1 X^2+X  X  0
 0  0  0  1  1 X^2 X^2+1  1  1  0 X^2+X+1  X  1 X^2+X+1  0  X  1 X+1 X^2+X+1 X^2  1 X^2+X
 0  0  0  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2  0  0 X^2 X^2 X^2  0 X^2

generates a code of length 22 over Z2[X]/(X^3) who´s minimum homogenous weight is 17.

Homogenous weight enumerator: w(x)=1x^0+144x^17+395x^18+796x^19+841x^20+1356x^21+1138x^22+1378x^23+836x^24+808x^25+319x^26+112x^27+49x^28+12x^29+4x^30+2x^31+1x^32

The gray image is a linear code over GF(2) with n=88, k=13 and d=34.
This code was found by Heurico 1.11 in 0.234 seconds.