  Single crystalline FeTe$_{0.61}$Se$_{0.39}$ with a sharp superconducting
transition at $T_{\textrm{c}} \sim$ 14 K is synthesized via slow furnace
cooling followed by low-temperature annealing. The effect of annealing on the
chemical and superconducting inhomogeneities is carefully characterized. We
also report resistivity, magnetization, and magneto-optical images of this
crystal. Based on the Bean model, critical current density is estimated to
exceed $1 \times 10^5$ A/cm$^2$ below 5 K under zero field. Weak fish-tail
effect is identified at lower temperatures.
