This is pretty simple. The key to making it even simpler is this line in the plot documentation:
"If X and Y are both matrices, then they must have equal size. The plot function plots columns of Y versus columns of X."
So we just need to form your matrix (call it A) into two matrices X and Y, with each line's data in a column.
AT = A.';
X = AT(:, 1:2:end);
Y = AT(:, 2:2:end);
I'm assuming that you actually meant your original matrix is 54 x 9011 (rows x columns), since otherwise there wouldn't be an even number of rows to pair for x and y. This will make 27 lines, which is doable. If you were making hundreds or thousands of lines, though, that would probably slow down your graphics system too significantly. Keep that in mind for the future.