intersect lines output points

I am trying to intersect a single line feature class to find where lines cross. unfortunatly this process picks up places where lines are "snapped" togeather as the vertexes are in the same location. any ideas how i can do this?

I am currently mapping storm sewer pipes and sometimes the pipes cross each other without connecting. in the past i was making a small kink in the pipe to represent the crossing but we want to swithc to a point symbol as it will reduce clutter/ be more visually accurate/ be pleasing to the eye...

thanks