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Councillor Tony Gosling, who was at the parade with his dog Reggy, said the promotion was "an absolute boost for the town".
In 2023 the club was handed a winding-up petition by HM Revenue and Customs, before local businesswoman Michelle Harness completed a takeover.
The trophy parade coincides with the start of the Stadium Weekender community music event at the Attis Arena and ends the club's 125th anniversary celebrations.
Lincolnshire on BBC Sounds latest episode of Look North here.