The generator matrix

 1  0  0  0  1  1  1  1 X^2+X  1  1  1  X X^2  0  1  1  X  1  1  1  X
 0  1  0  0  0  1 X^2 X^2+X+1  1 X^2+X X+1  1  1  X  1 X^2+X+1 X+1  1  0  1  X  0
 0  0  1  0  0  1 X^2+1 X^2 X^2+1  1 X^2+X X+1  1  1  0 X^2+1 X^2+X+1 X+1  1  X X+1  1
 0  0  0  1 X+1 X^2  1 X^2+1 X+1  X X^2+X  1  0  1 X+1 X^2+X+1 X^2+X+1  X X^2+1  X X^2+1 X+1
 0  0  0  0 X^2  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2  0  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+136x^17+472x^18+636x^19+1080x^20+956x^21+1496x^22+1186x^23+1141x^24+512x^25+365x^26+144x^27+50x^28+12x^29+2x^30+2x^31+1x^34

The gray image is a linear code over GF(2) with n=88, k=13 and d=34.
This code was found by Heurico 1.16 in 0.593 seconds.