Problem with Query on Taxonomy

This should works.

$args = array(
    'taxonomy' => 'your_taxonmy_name', // replace with your taxonomy name
);

$categories = get_categories( $args );

$ids = array(); 

// lets get all post IDs
foreach ( $categories as $category ) {
    $args = array(
        'cat' => $category->term_id,
        'post_type' => 'homepage', // your post type
        'posts_per_page' => '1',
        'post__not_in' => $ids, // don't want to any duplication
    );

    $query = new WP_Query( $args );

    if ( $query->have_posts() ) {
        $query->the_post();

        $ids[] = get_the_ID();
    }
}
wp_reset_postdata();

$args = array(
    'post__in' => $ids,
);

$query = new WP_Query( $args );

// your loop for echoing
if ( $query->have_posts() ) {
    while( $query->have_posts() ) {
        $query->the_post();

        // do what you want to
    }
}
wp_reset_postdata();