Is this changing-variance series stationary?

A series is $X_t = \varepsilon_t$ for $t = 1, 2, 3, \dots$, where the $\varepsilon_t$ are independent with mean 0, but the variance grows with time: $\operatorname{Var}(\varepsilon_t) = t$.

Is $\{X_t\}$ weakly stationary? Answer yes or no, and justify.