The generator matrix

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

generates a code of length 24 over Z2[X]/(X^3) who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+81x^22+93x^24+78x^26+1x^30+2x^36

The gray image is a linear code over GF(2) with n=96, k=8 and d=44.
This code was found by Heurico 1.16 in 0.00516 seconds.