Drupal 7 - Add a textarea to custom variables edit form

your_module.module

/**
 * Implements hook_variable_info().
 */
function your_module_variable_info($options) {

  $variables['your_variable'] = array(
    'title' => t('Title', array(), $options),
    'description' => t('Description.', array(), $options),
    'type' => 'text',
    'default' => 'Default value',
    'group' => 'my_variables_group',
    'element' => array(
      '#type' => 'text_format',
      '#base_type' => 'textarea',
      '#cardinality' => 1,
    ),
  );
}