The generator matrix

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

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+34x^22+58x^24+28x^26+4x^28+2x^30+1x^32

The gray image is a linear code over GF(2) with n=96, k=7 and d=44.
This code was found by Heurico 1.16 in 0.00434 seconds.