Originally it's Polish, not Russian. Your family may have lived on lands that were Russian empire at some point, but this surname is Polish, not Russian.
Check this out:
"Kublicki (or Pietuch, sometimes Piotuch)
- Polish noble coat of arms, family crest of formely a Lithuanian family, known in połockie lands since the 16th century and later in rzeczycki lands, a variation of Prus III coat of arms. According to S. Uruski in the połockie lands there was also a family of Kublicki with Ostoja coat of arms."
maybe in a town in the Polish-Lithuanian commonwealth
I think that's where your family comes from - the Polish-Lithuanian Commonwealth. After the partitions the Polish-Lithuanian Commonwealth ceased to exist and part of it's lands was taken by the Russian empire.
Do you, mean nobility or szlachta?
Nobility is the English word for "szlachta". "Szlachta" is a general term in Polish for all "ranks" of nobility: magnates, aristocracy, nobility, gentry or whatever:
"Szlachta" is also translated as "gentry", but judging by it's meaning that would be "szlachta zaściankowa" in Polish, I think.
Stanisław Kublicki's coat of arms/family crest was an old crest Ostoja and I'd say he defenitely belonged to "szlachta", rather than "szlachta zaściankowa". I don't know about Piotuch, but in that link I posted there are Polish insurrectionists fighting against Russia listed with surname "Piotuch" and one "Kublicki-Piotuch" - all of them are described as "szlachcic" (nobleman), so it looks like during the partitions that family still belonged to "szlachta" (nobility or gentry in thier case - I don't know).