The generator matrix

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

generates a code of length 22 over Z2[X]/(X^3) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+14x^20+40x^21+14x^22+48x^23+1x^24+8x^25+1x^26+1x^34

The gray image is a linear code over GF(2) with n=88, k=7 and d=40.
This code was found by Heurico 1.16 in 0.00242 seconds.