Answer: 215

Small Hint:

For each residue modulo $42$, find the smallest positive composite integer in that residue

Big Hint:

Once one number in a residue class is representable, every number $42$ larger in that class is representable

Solution:

A number in residue class $r\pmod {42}$ is representable once it exceeds the first positive composite in that class by a positive multiple of $42.$ Composite residues $r$ themselves supply that first value. For the remaining residues, suitable first composites are $$\begin{aligned}&0:42,\ 1:85,\ 2:44,\\&3:45,\ 5:215,\ 7:49,\\&11:95,\ 13:55,\ 17:143,\\&19:145,\ 23:65,\ 29:155,\\&31:115,\ 37:121,\ 41:125.\end{aligned}$$ The largest entry is $215,$ and $215-42,$ $215-84,$ $215-126,$ $215-168,$ and $215-210$ are all prime. Hence $215$ is not representable, while every larger integer is.