Autocovariance and autocorrelation functions

Question

Let us take the following $(X_t), \; t\in Z$ process: $X_t = \epsilon t\eta t$, where $\epsilon t$ and $\eta t$ are independent processes (from each other and in time as well), $\epsilon t$ is a white noise with $0$ expectation and $\sigma$ standard deviation, $P(\eta t = 0) = P(\eta t = 2) = 1/2 \; \forall t$. Is the process $X_t$ weakly stationary? Compute the autocovariance and autocorrelation functions.