I finally figured out how to do this.
Basically you have to use the placement.info file of your theme. You need to add <Place Fields_MediaLibraryPicker="Content:1" /> <!-- this adds the field.. -->
into your Summary.
So in my case my placement.info now contains this:
<Match DisplayType="Summary">
<Place Parts_Common_Metadata_Summary="-"/>
<Place Parts_Title="-"/>
<Place Fields_MediaLibraryPicker="Content:1" /> <!-- this adds the field.. -->
</Match>