In db.js, modify the _product_search_string function as you need. For example, if you want to add searching for default_code also, then the function can be written as,

_product_search_string: function(product){
            var str = '' + product.id + ':' + product.name;
            if(product.ean13){
                str += '|' + product.ean13;
            }
            if(product.default_code){
                str += '|' + product.default_code;
            }
            var packagings = this.packagings_by_product_id[product.id] || [];
            for(var i = 0; i < packagings.length; i++){
                str += '|' + packagings[i].ean;
            }
            return str + '\n';
        },

And in the models.js file, in the function load_server_data, in the delf.fetch part of product.product, add the field default_code.

 return self.fetch(
  'product.product', 
   fields=['name', 'list_price','price','pos_categ_id', 'taxes_id', 'ean13', 'default_code',
   'to_weight', 'uom_id', 'uos_id', 'uos_coeff', 'mes_type', 'description_sale', 'description'],
    domain=[['sale_ok','=',true],['available_in_pos','=',true]],
  {pricelist: self.get('shop').pricelist_id[0]} // context for price
    );