Using the Roots of a Polynomial

Calculus Level 5

What is the smallest degree of a non-constant complex polynomial $f(x)$ , such that the only roots of $f$ are $0$ , $2$ and $3$ , and the derivative of $f(x)$ is divisible by $8x^2-24x+7$ ?

Details and assumptions

All roots of $f(x)$ , real or complex, are in the set $\{0,2,3\}$ .