I do not agree with a judicial judgment. Can the Síndic appeal this decision?

No. The Spanish Constitution safeguards the judicial independence principle which provides that justice is administrated only by courts and tribunals. According to the Ley Reguladora del Síndic (Síndic‘s regulatory law), the Síndic cannot investigate those cases pending judgement. If you want to appeal a court decision you will have to lodge a judicial review according to the procedural laws.

However, you can file a complaint against the running of Justice Administration (for example, delay in the judicial processing).