The maximum value for fuzziness that Elasticsearch supports is 2. I am surprised it does not return an error indicating this.
It is worth noting that the query you specified witha 4 letter string and fuzziness of 4 would (if there was not a limitation in place) match any word with 4 or less letters as well as a lot of words that are up to 4 characters longer assuming they contain some of the characters in the string. This would return very useful results.