  Using Zeilberger's algorithm, we here give a proof of the supercongruence $$
\sum_{n=0}^{\frac{p^r-3}{4}}(8n+1)\frac{\left(\frac{1}{4}\right)_n^4}{(1)_n^4}\equiv
-p^3
\sum_{n=0}^{\frac{p^{r-2}-3}{4}}(8n+1)\frac{\left(\frac{1}{4}\right)_n^4}{(1)_n^4}
~~(\text{mod }p^{\frac{3r-1}{2}}),$$ for any odd integer $r>3$. This extends
the third conjectural supercongruence of (G.3) of Swisher to modulo higher
prime powers than that expected by Swisher.
