BLUEREDGOLDEGGSFEATHERSFEATHERS
Brachylog, 25 bytes

hsS&amp;t⊇.g;Sz{∋ʰ}ᵐhᵍ{tᵐc}ᵐp


Try some of the faster test cases online!

Extremely slow brute force, that I haven't verified on the longer test cases yet. It wouldn't surprise me if a clever implementation of a smarter algorithm turns out considerably shorter. Takes input as a list [entry,codes] through the input variable and outputs through the output variable if it succeeds. Seems to comply fully with the spec to the extent to which I've tested it at all.

The exact nature of the brute force is that for every substring of the entry (until there's a match), it tries every subset of the codes until it's possible to assign one code to each letter of the substring such that the letters assigned to each code taken in order form that code. The worst case complexity, where the worst case is failure, is something vaguely along the lines of \$O(x^22^yy^x)\$ with \$x\$ the length of the entry and \$y\$ the number of codes.