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You can't do it without a module.
You need to write a module and use the displayProductListReviews hook, or create your own hook and build it into ./themes/classic/templates/catalog/_partials/miniatures/product.tpl

And in order not to show it in the product detail, you will need to treat the pages as an index and category in the hook. This is written either to the TPL template or to the module.
E.g. custom hook and Home and Category pages.

[color=#FF0000]Totom is just a sample, it's not functional code !!![/color]

TPL file product.tpl:

{if $page.name == 'index' || $page.name == 'category'}
	{block name='product_carrier'}
          {hook h='displayProductListCarrier' id_product=$product.id_product}
    {/block}
{/if}

PHP module:

public function install() 
    {
        $this->installConfiguration();
        
        if (Shop::isFeatureActive())
        {
            Shop::setContext(Shop::CONTEXT_ALL);
        }
        
        if (!parent::install())
        {
            return false;
        }
	
		
		$hook = new Hook();
        $hook->name = 'displayProductListCarrier';
        $hook->title = $this->l('Hook show carriers');
        $hook->description = $this->l('This is a hook shoe carriers!');
        $hook->position = 1;
        $hook->add();
        $this->registerHook('displayProductListCarrier');
        
        return true;
    }

public function hookDisplayProductListCarrier($params) 
    {
	$template = '';	
	$getProductCarriers = Db::getInstance()->executeS('
            SELECT c.*
            FROM `' . _DB_PREFIX_ . 'product_carrier` pc
            INNER JOIN `' . _DB_PREFIX_ . 'carrier` c
                ON (c.`id_reference` = pc.`id_carrier_reference` AND c.`deleted` = 0)
            WHERE pc.`id_product` = ' . (int) $params['id_product'] . '
                AND pc.`id_shop` = ' . (int) $this->Context::getContext()->shop->id);

		if ($getProductCarriers){
			$template .= '<div style="display:block">';
			foreach ($getProductCarriers as $carrier){
				$template .= '<span>'.$carrier['name'].'</span><br>';	
			}
            $template .= '</div>';

			return $template;
		} else {
			return;
		}

    }