Inline colorbox & linebreaks

Question

First and foremost, I have found some solutions here, here, and there but they seem overly complicated for what I am trying to accomplish.

Problem

I am trying to somewhat reproduce the code environment "markdown-style" in LaTeX. I used a colorbox in conjunction with texttt to get a pretty satisfying look but it does not allow line breaks and thus breaks everything when used with paths or long lines.

Question

It is my understanding that colorbox cannot be used to output multiple lines. What could help me achieve this while keeping the code fairly clean?

MWE

\documentclass[draft]{article}
\usepackage[french]{babel}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage{lipsum}
\usepackage[framemethod=tikz]{mdframed}
\usepackage{geometry}
\usepackage{pdftexcmds}
\usepackage{xcolor}
\newcommand{\code}[1]{\colorbox{black!30}{\textcolor{black!90}{\texttt{\detokenize{#1}}}}}
\newcommand{\codeA}[1]{\colorbox{black!30}{\textcolor{black!90}{\texttt{#1}}}}
\begin{document}
test \code{code} test \code{+}

\lipsum[1]

\codeA{\lipsum[2]}
\end{document}