Largest smallest gap
05AB1E, score: 22 49 69 (5 4 bytes)
ê¥êн

Uses the 05AB1E encoding, where the bytes have the codepoints [234,165,234,14] (ê¥ are 69 apart).
+27 score by porting @Arnauld's approach of sorting.
+20 score (and even -1 byte at the same time) thanks to @Grimmy.
Try it online or verify all test cases.
Explanation:

ê     # Sort and uniquify the (implicit) input-list (in ascending order)
 ¥    # Get the deltas of this sorted list
  ê   # Sort and uniquify this again
   н  # Pop this list and push its first item
      # (which is output implicitly as result)