Here is the proposed solution, i suggest that you use the polar coordinates as the following :
The corresponding figure is attached below :
As the vector z is in decibel, you can search for the indexes of z that are above max(z)-3dB :
Next you plot the matrix with corresponding indexes :
The result is in the second figure :
The beam width is in the square of 20^2 units of surface, you can deduce the angular value .