For the $^{68}$Zn + $^{112}$Sn reaction the Coulomb parameter is equal to 1500 that is close to the threshold value for the appearance of quasifission process. It was found that mass-energy distributions of the reaction fragments differ significantly from those obtained in the $^{36}$Ar + $^{144}$Sm reaction leading to the formation of the same composite system of $^{180}$Hg at similar excitation energies of about 50 MeV. In the case of the reaction with $^{68}$Zn ions, the mass distribution of fissionlike fragments has a wide two-humped shape with maximum yields at 70 and 110 u for the light and heavy fragments, respectively, instead of 80 and 100 u observed in the fission of $^{180}$Hg formed in the $^{36}$Ar + $^{144}$Sm reaction. The difference is explained by an unexpectedly large contribution (more than 70%) of quasifission in the case of the $^{68}$Zn + $^{112}$Sn reaction.
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