mat = [1 1 0 1; 0 0 1 0; 1 1 0 1; 1 0 0 0];  % Your sample matrix
[r, c] = size(mat);                          % Get the matrix size
imagesc((1:c)+0.5, (1:r)+0.5, mat);          % Plot the image
colormap(gray);                              % Use a gray colormap
axis equal                                   % Make axes grid sizes equal
set(gca, 'XTick', 1:(c+1), 'YTick', 1:(r+1), ...  % Change some axes properties
         'XLim', [1 c+1], 'YLim', [1 r+1], ...
         'GridLineStyle', '-', 'XGrid', 'on', 'YGrid', 'on');