The Gorgie club entered administration last month, which brought a 15-point deduction and a registration embargo with further possible sanctions to follow.
"I think it would be the biggest achievement in the club's history if we were able to overturn this," the Scotland defender said.
"We are young and it is going to be difficult but we have the chance to make ourselves heroes at this club and that's what you want as a footballer. You would rather be going for cups and titles, obviously, but this would be just as big."
Manager Gary Locke has watched a whole team of players depart the club, including experienced defenders Andy Webster and Marius Zaliukas and striker John Sutton, and has been left with a squad packed with youngsters.
Some eyebrows were raised when Wilson resisted the temptation to join the Tynecastle exodus. The former Rangers player agreed a three-year deal with the Jambos following a loan move from Liverpool last season but could have moved on when Hearts entered administration.
A loophole allowed him to get around the consequent signing embargo imposed but, along with several other players, he took a wage cut to stay at the club.
Asked if it might have been better to go somewhere more stable, Wilson replied: "People have said that to me and I had other offers but I made the commitment about a month and a half ago to stay here and I made a lot of changes in my life for that.
"I had bought a house and was settled and didn't want to uproot again. Obviously, I took a wage cut to stay and was more than happy to do so to help in any way I could.
"I had been really happy here for six months and I get on so well with the manager and the boys at the club. So you don't just trade that for a bit of uncertainty."