The generator matrix

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

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+148x^19+143x^20+188x^21+130x^22+176x^23+83x^24+96x^25+12x^26+28x^27+13x^28+4x^29+2x^30

The gray image is a linear code over GF(2) with n=88, k=10 and d=38.
This code was found by Heurico 1.11 in 17.3 seconds.