Binding in listbox with textblocks not working - wpf

Question

I have the following xaml code:
<ListBox Foreground="{Binding MyColor, Converter={local:ColorConverter}}" ItemsSource="{Binding LogCollection, Mode=TwoWay}" Grid.Row="1">
</ListBox>
This changes the foreground color for the entire listbox, so I modified the code in this way:
<ListBox ItemsSource="{Binding LogCollection, Mode=TwoWay}" Grid.Row="1">
<ListBox.ItemTemplate>
<DataTemplate>
<TextBlock Foreground="{Binding MyColor, Converter={local:ColorConverter}}" Text="{Binding}"/>
</DataTemplate>
</ListBox.ItemTemplate>
</ListBox>
In this way I wanted to set the foreground for an item instead for the entire listbox, but it is not working. How do I find the right datacontext ? MyColor is a property on my MainViewModel.
LATER EDIT WITH THE SOLUTION
Jens's answer was the one that showed me where I was wrong. Instead of storing simple message log strings in the ObservableCollection, I created a new class (LogItems) which contains a Message and a Color members. Now the LogCollection is typeof LogItems instead of strings.
I populate the listbox with the following code in my viewmodel:
LogItems logitem = new LogItems(myMessage, myColor);
LogCollection.Insert(0, logitem);
And the view has the following form. Also it doesn't require anymore to use RelativeSource, because the datacontext is the same.
<ListBox ItemsSource="{Binding LogCollection, Mode=TwoWay}" Grid.Row="1">
<ListBox.ItemTemplate>
<DataTemplate>
<TextBlock Foreground="{Binding Path=Color, Converter={local:ColorConverter}}" Text="{Binding Path=Message}"/>
</DataTemplate>
</ListBox.ItemTemplate>
</ListBox>
Thank you all for your answers which lead me to this solution.

Answer 1

The DataContext of generated container in a listbox is automatically set to the corresponding item, therefore your Binding does not find the Property MyColor. You need to use a RelativeSource binding to bind to the DataContext of the containing list:
<TextBlock Foreground="{Binding DataContext.MyColor,
RelativeSource={RelativeSource
Mode=FindAncestor,
AncestorType={x:Type ListBox}},
Converter={local:ColorConverter}}"
Text="{Binding}"/>