The generator matrix

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

generates a code of length 22 over Z2[X]/(X^3) who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+106x^12+56x^14+470x^16+608x^18+4022x^20+5840x^22+4048x^24+608x^26+470x^28+56x^30+89x^32+10x^36

The gray image is a linear code over GF(2) with n=88, k=14 and d=24.
This code was found by Heurico 1.16 in 1.63 seconds.