OPM 2023 Problem 6

A rectangular board, where in each square there is a symbol, is said to be magnificent if, for each line $L$ and for each pair of columns $C$ and $D$ , there is on the board another line $M$ exactly equal to $L$ , except in columns $C$ and $D$ , where $M$ has symbols different from those of $L$ . What is the smallest possible number of rows on a magnificent board with $2023$ columns?