MWE:
\documentclass{article}
\usepackage[stable]{footmisc}
\usepackage{footnote}
\usepackage{caption}
\usepackage{hyperref}
\usepackage{listings}\usepackage{genmpage}
\begin{document}
\begin{minipage}{\linewidth}
\centering
\begin{lstlisting}[frame=single]
mycode;
\end{lstlisting}
\captionof{figure}{Short.}
\end{minipage}
\medskip
\begin{minipage}{\linewidth}
\centering
\begin{lstlisting}[frame=single]
mycode;
\end{lstlisting}
\captionof{figure}{Multiple Words. Multiple Words. Multiple Words. Multiple Words. Multiple Words. Multiple Words. Multiple Words. Multiple Words. Multiple Words. Multiple Words. Multiple Words. Multiple Words.}
\end{minipage}
\end{document}
In the first example, the caption is aligned perfectly in the middle. However, on the second one it isn't aligned in the center at all. It looks like it's left justified despite having a \centering on it.
Edit:
Using figures to encapsulate lstlistings cause minipages to be out of order.
\documentclass{article}
\usepackage[stable]{footmisc}
\usepackage{footnote}
\usepackage[justification=centering]{caption}
\usepackage{hyperref}
\usepackage{listings}
\usepackage{genmpage}
\usepackage{graphicx}
\begin{document}
\begin{minipage}{\linewidth}
\centering
\includegraphics[width=\linewidth]{example-image-a.jpg}
\captionof{figure}{Figure at \#1.}
\end{minipage}
\begin{figure}
\begin{lstlisting}[frame=single]
Figure at #2;
\end{lstlisting}
\caption{Multiple Words. Multiple Words. Multiple Words. Multiple Words. Multiple Words. Multiple Words. Multiple Words. Multiple Words. Multiple Words. Multiple Words. Multiple Words. Multiple Words.}
\end{figure}
\begin{figure}
\begin{lstlisting}[frame=single]
Figure at #3;
\end{lstlisting}
\caption{Multiple Words. Multiple Words. Multiple Words. Multiple Words. Multiple Words. Multiple Words. Multiple Words. Multiple Words. Multiple Words. Multiple Words. Multiple Words. Multiple Words.}
\end{figure}
\end{document}
The use of minipages for pictures is derived from here: http://tex.stackexchange.com/a/54449/161008
The use of figures for listings is derived from here: https://tex.stackexchange.com/a/19668/161008

minipageseems unnecessary there, however – Apr 18 '18 at 19:48minipagehas the good side effect to suppress theoutside box or environmentwarning – samcarter_is_at_topanswers.xyz Apr 18 '18 at 19:53figure, you should also give floating specifier, such as\begin{figure}[htbp]. – samcarter_is_at_topanswers.xyz Apr 18 '18 at 20:26