How to search for a DNA sequence in a genome on ENA (European Nucleotide Archive)?
While it is much better/easier to download and do the exact search on your own, it is possible to do something similar, online. You can use NCBI-BLAST and increase the word length and mismatch/gap penalty. It also allows restricting the subject space; you can even align two sequences. The BLAST on ENA does not have much flexibility (subject restriction/word length). Perhaps you can look for a duplicate sequence on NCBI. 

If this genome is available on UCSC genome browser then you can use BLAT too. However, it only accepts sequences larger than 19nt.