Poisson fiber bundles

Question

Let $E$ be a vector bundle and $W\in \Lambda^2 (TM \otimes E) \otimes E$. I define a Poisson bracket over sections of $E$:
$$\{ s,s'\}=W(\nabla s,\nabla s')$$
With a connection $\nabla$ over $E$.
With conditions over $W$, we have the Jacobi identities:
$$\{f,\{g,h\}\}=\{\{f,g\},h\}+\{g,\{f,h\}\}$$
Can we quantize the structure?