An example is given in my paper with T.Tibor Beke, https://arxiv.org/pdf/1005.2910.pdf (see
Abstract elementary classes and accessible categories, Annals Pure Appl. Logic 163 (2012), 2008-2017, doi:10.1016/j.apal.2012.06.003, arXiv:1005.2910.
see Remark 3.2(4)). This is what Reid Barton indicated.