Export data/map as a shapefile or Geotiff for external post-processing

I feel incredibly stupid for asking, but I have been battling with this issue for the last couple of days without getting any wiser.

I have managed to plot my data on a map using geoshow, but cannot figure out how to export the data/map as a shapefile for further processing in external software. I would be very grateful for any advice.

My code is:

% I am originally working with European Climate Assessment and Datasets - E-OBS gridded dataset (0.44 degree rotated pole grid)
% Link to website hosting data: https://eca.knmi.nl/
% Below is a rough example dataset I tried to create to simulate my actual dataset and assist with this question
forMatA = (25:0.44:75)
forMatB = (-40:0.44:75)
mineB=forMatB(100:183); mineA = forMatA(60:103);

mineForMatlabA= randi([1 300],[56,51,12]);
VarMat={'mineForMatlabA'};
tit={'June'};

forMatA = (25:0.44:75)
forMatB = (-40:0.44:75)
mineB=forMatB(100:183); mineA = forMatA(60:103);

for x=1:1
    figure(x)
% Specify lat, lon boundary
    latlim=[45.7618 71.9799];
    lonlim=[-8.5147 52.8165];
    MapLat=mineA;
    MapLon=mineB;
    
% Define basemap for specified lat, lon boundaries
    usamap(latlim, lonlim);
    MAP = geoshow('landareas.shp', 'FaceColor', [0.5 0.5 0.5]);
    
    varx=eval(VarMat{x});
    Z(:,:)=nanmean(varx(:,:,:),3);
     
     surfm(MapLat,MapLon,Z)
   
framem off; gridm off; mlabel off; plabel off
title(tit{x},'FontSize',20,'FontWeight','bold');
set(get(gca,'title'),'Color','k', 'FontSize',14,'FontWeight','bold') % title('30-min Observed VS. Modelled Evapotranspiration in 1997','FontSize',20,'FontWeight','bold');
end

Regards

J