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Time Remaining $02$:$03$:$30$

A certain computer program is designed to solve a $33$ grid of digits, ranging from $0$ to $9,$ in $4\mathrm{.}0$ seconds. The average time to solve a matching puzzle is directly proportional to the total number of possible choices. Which of the following approximates the average length of time it would take the computer to solve a similar $44$ grid of numbers ranging from $0$ to $9?$

$($Note: numbers may be repeated in each grid square when solving the puzzle. Assume the computer program runs continuously and without interruption.$)$

$1$ month

$1$ year

$10$ years

$1$ day