The generator matrix

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

generates a code of length 24 over Z2[X]/(X^3) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+212x^16+388x^18+1488x^20+3472x^22+5190x^24+3544x^26+1600x^28+272x^30+195x^32+4x^34+16x^36+2x^40

The gray image is a linear code over GF(2) with n=96, k=14 and d=32.
This code was found by Heurico 1.16 in 22 seconds.