Many software engineers direct their talents towards software systems which do not fall into traditional definitions of safety critical systems, but are integral to society (e.g., social media, expert advisor systems). While codes of ethics can be a useful starting point for ethical discussions, codes are often limited in scope to professional ethics and may not offer answers to individuals weighing competing ethical priorities. In this paper, we present our vision for improving ethics education in software engineering. To do this, we consider current and past curricular recommendations, as well as recent efforts within the broader computer science community. We layout challenges with vignettes and assessments in teaching, and give recommendations for incorporating updated examples and broadening the scope of ethics education in software engineering.