smc

Neither of the digits $4$, $6$, and $8$ can be a units digit of a prime. Therefore the sum of the set is at least $40+60+80+1+2+3+5+7+9=207$. We can indeed create a set of primes with this sum, for example the following sets work: $\{41,67,89,2,3,5\}$ or $\{43,61,89,2,5,7\}$. Thus the answer is $207⟹\boxed{207}$.