The home side resumed and were finally all out for 385 with Boje making 103.
In reply, Warwicks were poor in the final session of the second day. Opener Ian Westwood made a combined total of 13 before Cov kid Ian Bell came in to hit 41 before he was given out lbw off the bowling of Boje.
Jon Trott was run out for six, then England international Tim Ambrose was dismissed for 15 with Ant Botha who had made eight following soon after.
Michael Powell made 24 but at the close Warwicks were 129-7 after 57 overs.