How assign current class at home page by core

The problem is not when I click on the item menu home, but when I open the first time the site;
I use plugin Static Front Page for the home; but when I open the first time the site (in localhost)
the home not have the current class.
So I want to change the core, the template-functions-post.php (row 416 about)

This is the code:
$css_class = ‘page_item’;
1- if ( $page_id == $queried_obj->ID )
2- $css_class .= ‘ current_page_item’;

$output .= $indent . ‘<li class=”‘ . $css_class . ‘”>#a href=”‘ . get_page_link($page_id) . ‘” title=”‘ . wp_specialchars($title) . ‘”>’ . $title . ‘#/a>’;

the row 1 and 2 when I have home page not work;
If I add this code:
$css_class = ‘page_item’;
1- if ( $page_id == $queried_obj->ID )
2- $css_class .= ‘ current_page_item’;
3 if (is_home())
$css_class .= ‘ current_page_item’;

It insert the class current_page_item on all the item and not only in the home page;

Any solutions?

————————————————-
This is is the solution that I not want use because the home page isn’t more inner the list but external
<?php if (is_home()): ?>
<li class=”current_page_item”>;
<?php wp_list_pages(‘title_li=’); ?>
<?php else : ?>

• #/a>#/a>

#/a><?php wp_list_pages(‘title_li=’); ?>
<?php endif; ?>#/a>#/a>

(I use # only how sobstitute > or < that change the format of the post)