template-grid-archive.php

<?php
/* Template Name: Grid Archive */

/**
 * Category Loop
 * 
 */
function be_category_loop() {
  global $post, $wp_query;
  $args = array(
    'posts_per_page' => 20,
    'post_type' => 'post',
    'paged' => get_query_var( 'paged' ),
    'cat' => (int) get_post_meta( $post->ID, 'query_args', true ),
  );
  $wp_query = new WP_Query( $args );
    if( $wp_query->have_posts() ):
 
		while( $wp_query->have_posts() ): $wp_query->the_post(); global $post;
 
			$classes = 0 == $wp_query->current_post || 0 == $wp_query->current_post % 2 ? 'post one-half first' : 'post one-half';
			echo '<div class="' . $classes . '">';
			echo '<h2 class="entry-title"><a href="' . get_permalink() . '">' . get_the_title() . '</a></h2>';
			echo '<div class="entry-content">';
			echo '<a href="'.get_permalink().'">' . get_the_post_thumbnail( null, 'grid-thumbnail' ) . '</a>';
			echo '</div>';
			echo '</div>';
		
		endwhile;
		genesis_posts_nav();
	endif;
 
	wp_reset_query();
}
add_action( 'genesis_loop', 'be_category_loop' );
remove_action( 'genesis_loop', 'genesis_do_loop' );

genesis();

Assumptions:

• You're storing the category ID in the custom field 'query_args'
• The post thumbnail size you want is 'grid-thumbnail'
• You want 20 posts per page, and for this to be paginated.

Note: This really shouldn't be done through a custom page template. Use the standard category archive (template: category.php) and you won't need to do a custom query.