The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+1x^22+10x^23+1x^24+2x^25+1x^26

The gray image is a linear code over GF(2) with n=88, k=4 and d=44.
This code was found by Heurico 1.16 in 0.00203 seconds.