You can use this
$_attributeValue = $_product->getResource()->getAttribute($_code)->getFrontend()->getValue($_product);
For your case you need to create plugin for \Magento\Checkout\CustomerData\DefaultItem::getItemData and extend data.
public function getItemData(Item $item)
{
$this->item = $item;
return \array_merge(
['product_type' => $item->getProductType()],
['product_attribute' => $attributeValue]
$this->doGetItemData()
);
}
After that in template web/template/minicart/item/default.html new data will be accessible
<strong class="product-item-name">
<!-- ko if: product_has_url -->
<a data-bind="attr: {href: product_url}, text: product_name"></a>
<!-- /ko -->
<!-- ko ifnot: product_has_url -->
<!-- ko text: product_name --><!-- /ko -->
<!-- /ko -->
<label data-bind="text: product_attribute"></label>
</strong>
refer this link for which file you have to override or this link for where you have to add product attribute value.
May be it will work.