  It was well known that there are $e$-particles and $m$-strings in the
3-dimensional (spatial dimension) toric code model, which realizes the
3-dimensional $\mathbb{Z}_2$ topological order. Recent mathematical result,
however, shows that there are additional string-like topological defects in the
3-dimensional $\mathbb{Z}_2$ topological order. In this work, we construct all
topological defects of codimension 2 and higher, and show that they form a
braided fusion 2-category satisfying a braiding non-degeneracy condition.
