There are nameservers not listed at your nameservers:
Nameservers on separate class C's
Nameservers are in a different networks.
All of your NS records appear to use public IPs.
SOA record is:
All your nameservers agree that your SOA serial number is 2016120201 That means that all your nameservers are using the same data.
SOA (Start of Authority) record states that your master (primary) name server is: nsp52797.dns-privadas.es, but that server is not listed at the parent servers.
SOA serial number is: 2016120201 This appears to be in the recommended format of YYYYMMDDnn, where 'nn' is the revision. This number must be incremented every time you make a DNS change.
SOA Retry interval is : 10800 seconds. This seems OK. (Values about 3600-7200 seconds is good if not using DNS NOTIFY; RFC1912 2.2 recommends a value between 1200 to 43200 seconds (20 minutes to 12 hours)). This value determines how often secondary/slave nameservers check with the master for updates.
SOA Retry interval is : 3600 seconds. This seems OK. (Values about 120-7200 seconds is good). The retry value is the amount of time your secondary/slave nameservers will wait to contact the master nameserver again if the last attempt failed.
SOA Expire time is : 604800 seconds. This seems OK. (Values 604800 to 2419200 seconds (1-4 weeks) is good). RFC1912 suggests 2-4 weeks. This is how long a secondary/slave nameserver will wait before considering its DNS data stale if it can't reach the primary nameserver.
SOA Expire time is : 86400 seconds. This seems OK. (about 300 to 86400 seconds or 5 min - 24 hours is good). RFC2308 suggests a value of 1-3 hours. This value used to determine the default (technically, minimum) TTL (time-to-live) for DNS entries, but now is used for negative caching.
Trace to barnahosting.net
lookup barnahosting.net at A.ROOT-SERVERS.NET(126.96.36.199) 5 ms
A.ROOT-SERVERS.NET(188.8.131.52) refer to e.gtld-servers.net(184.108.40.206)
lookup barnahosting.net at e.gtld-servers.net(220.127.116.11) 40 ms
e.gtld-servers.net(18.104.22.168) refer to ns1.barnahosting.net(22.214.171.124)
lookup barnahosting.net at ns1.barnahosting.net(126.96.36.199) 98 ms
got A record 'barnahosting.net IN A 188.8.131.52' from barnahosting.net(184.108.40.206)