Hitting Time with State-Dependent Self-Loops

A Markov chain on $\{0, 1, 2, 3\}$ has transition probabilities: from state $i$ ($0 \le i \le 2$), the chain stays at $i$ with probability $\frac{i}{4}$, moves to $i+1$ with probability $1 - \frac{i}{4}$. State $3$ is absorbing.

Compute $E[T_3 \mid X_0 = 0]$.