Sometimes a word does have multiple "valid" pitch accent patterns. Daijirin often lists multiple pitch downstep numbers for terms that have them, like, say, the entry for とらまえる, which lists patterns 4 and 3. That said, the Daijirin entry for ここのか only lists pitch pattern 4, with a downstep after the fourth mora.
Checking in my local copy of the NHK アクセント辞典, they list two patterns -- 4 for the noun, and 0 (no downstep) for the adverb. However, a bit confusingly, both entries (noun and adverb) include the same sample sentence:
It seems that Daijirin wound up using one pattern, and OJAD the other, but if the NHK is anything to go by, it looks like both patterns 4 and 0 are recognized as correct.