The synopsis for Imager::Heatmap can not be run as is. It doesn't create $base_img, it doesn't show how to properly use matrix, etc. So it is no surprise that what you ended up with didn't work.

Try this as a starting point. It uses your data and creates a png file in the current directory.

#!/bin/env perl
use strict;
use warnings;

use Imager::Heatmap;

my $hmap = Imager::Heatmap->new(
    xsize  => 640,        # Image width
    ysize  => 480,        # Image height
    xsigma => 10,         # Sigma value of X-direction
    ysigma => 10,         # Sigma value of Y-direction
);

# @point_datas should be: ( [ x1, y1, weight1 ], [ x2, y2, weight2 ] .
+.. )
my @point_datas = ( [ 10, 20, 50 ], [ 20, 40, 70 ] );

# Add point datas to construct density matrix
$hmap->insert_datas(@point_datas); 

# After adding datas, get heatmap as Imager instance.
my $img = $hmap->draw;

# create png file in current directory
$img->write( file => './hm.png' );
[download]

Here's the generated heatmap image.