The generator matrix

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

generates a code of length 22 over Z2[X]/(X^3) who´s minimum homogenous weight is 19.

Homogenous weight enumerator: w(x)=1x^0+138x^19+149x^20+206x^21+132x^22+168x^23+59x^24+96x^25+28x^26+30x^27+15x^28+2x^29

The gray image is a linear code over GF(2) with n=88, k=10 and d=38.
This code was found by Heurico 1.16 in 0.055 seconds.