The generator matrix

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

generates a code of length 22 over Z2[X]/(X^3) who´s minimum homogenous weight is 18.

Homogenous weight enumerator: w(x)=1x^0+10x^18+15x^20+32x^21+144x^22+32x^23+11x^24+5x^26+5x^28+1x^42

The gray image is a linear code over GF(2) with n=88, k=8 and d=36.
This code was found by Heurico 1.16 in 0.00708 seconds.