To convert a list field column to use checkboxes add the php excluding the first line to your theme functions.php file. The JavaScript can be placed between script tags in a HTML field on the form.

change_col_to_checkboxes.php

<?php
// format: gform_column_input_content_FORMID_FIELDID_COLUMN
add_filter( 'gform_column_input_content_524_2_2', 'change_column_to_checkbox', 10, 6 );
function change_column_to_checkbox( $input, $input_info, $field, $text, $value, $form_id ) {
    $input_field_name = "input_{$field['id']}[]";
    $tabindex = GFCommon::get_tabindex();
    $new_input = "<div class='ginput_container'><ul class='gfield_checkbox'>" .
        "<li><input type='checkbox' {$tabindex} value='First Choice' /><label>First Choice</label></li>" .
        "<li><input type='checkbox' {$tabindex} value='Second Choice' /><label>Second Choice</label></li>" .
        "</ul><input type='hidden' name='{$input_field_name}' value='' /></div>";
    return $new_input;
}

list_field_checkboxes.js

jQuery( '.ginput_list' )
    .on( 'click', 'input[type=checkbox]', function() {
        var $cell = jQuery( this ).parents( 'td' ),
            $checked = $cell.find( 'input[type=checkbox]:checked' ),
            $value = '<ul>';
        $checked.each( function() {
            $value = $value + '<li>' + jQuery( this ).val() + '</li>';
        });
        $value = $value + '</ul>';
        $cell.find( 'input[type=hidden]' ).val( ( $checked.length > 0 ) ? $value : '' );
    })
    .on( 'click', '.add_list_item', function() {
        jQuery( this ).parents( 'tr' ).next()
            .find( 'input[type=checkbox]' )
            .each( function() {
                var $this = jQuery( this ),
                    $label = $this.next( 'label' ).text();
                $this.prop( 'checked', false ).val( $label );
            })
    });