By way of comparison (and I'm not sure how to go about searching for the next highest score across both innings of a game so this is as much as I can be bothered to do), in the very first test innings when Charles Bannerman set the record for Highest Proportion of Runs Scored in an Innings, the next highest score after his 165 was 18* by Tom Garrett.A score of 106, in a Test where the next highest score (across BOTH of his side's innings) is 15, is quite something, statistically.
The next highest score across both Australian innings was 20 by Tom Horan.
AUS vs ENG, England tour of Australia 1876/77, 1st Test at Melbourne, March 15 - 19, 1877 - Full Scorecard
Get cricket scorecard of 1st Test, AUS vs ENG, England tour of Australia 1876/77 at Melbourne Cricket Ground dated March 15 - 19, 1877.
www.espncricinfo.com
It's worth looking through the player profile pages to see the hat/facial hair combos the players rocked back then.
I also note that they've counted the balls faced by each batter in every innings except the first, which may suggest the scorer hadn't turned up for the start of the game.