This is the 4868th most frequent Polish word.
otwartego
"Otwartego" means "open" (masculine singular genitive or accusative form).
The word 'otwartego' is used here in the genitive case to describe 'open mind' in reference to company.
Lubię przebywać w towarzystwie otwartego umysłu.
I like being in the presence of an open mind.
'Otwartego' modifies the noun 'shape' in a descriptive genitive case indicating the form.
Drzwi do sali pozostały otwartego kształtu.
The doors to the hall remained of an open shape.
The term 'otwartego' is applied to 'spirit' in the genitive form conveying an appreciative tone for openness.