\documentclass[tikz,border=10pt]{standalone}
\usetikzlibrary{braids}

\begin{document}
\begin{tikzpicture}[scale=0.4, every node/.style={scale=0.4}]
\pic[
  rotate=90,
  line width=1.5pt,
  braid/control factor=0,
  braid/nudge factor=0,
  braid/gap=0.11,
  braid/number of strands = 4,
  braid/strand 1/.style={blue},
  braid/strand 2/.style={orange},
  braid/strand 4/.style={purple},
  name prefix=braid,
] at (-0.25,0) {braid={
s_3s_2s_1-s_3s_2s_3s_3s_2s_1-s_3s_2s_1^{-1}-s_3s_2^{-1}s_1^{-1}-s_3^{-1}s_2^{-1}s_1^{-1}-s_3^{-1}s_2^{-1}s_1^{-1}-s_3^{-1}s_2^{-1}s_3^{-1}
}};
\end{tikzpicture}
\end{document}