Sorry for the delay in sending this.

By comparing Firefox_correctly_shows.JPG and IE_11_wrap.JPG, I can see that the caption of column header overlapping the next column header in IE browser.

Try to add CustomRules in HeaderStyle and set its value as shown in the following snippet code.

<ISWebGrid:WebGrid ID="WebGrid1" runat="server" ...>
    <RootTable DataKeyField="CODICE">
        <Columns>
            <ISWebGrid:WebGridColumn Caption="CODICE" DataMember="CODICE"
                Name="CODICE" Width="100px">
            </ISWebGrid:WebGridColumn>
            ...
        </Columns>
    </RootTable>
    <LayoutSettings ...>
        ...
        <HeaderStyle ... CustomRules="text-overflow:ellipsis;overflow:hidden;" />
    </LayoutSettings>
</ISWebGrid:WebGrid>

This should helps.