Hi C Deho
I don't think there is a mistake in your approach; and I don't have MatLab so really helping is a little out of the question. Can I instead change course and point you here:
https://mapdl.docs.pyansys.com/version/stable/examples/gallery_examples/03-general-fea/00-how_finite_element_works.html#sphx-glr-examples-gallery-examples-03-general-fea-00-how-finite-element-works-py
It's an example from a popular FEA textbook that compares the Mechanical APDL version of a plane quadratic element to one written from scratch using Python and NumPy. Perhaps you could practice with this and implement it in MatLab as well. Then if all goes well move onto the tetrahedral element.
Mike
You are navigating away from the AIS Discovery experience