Should you learn how to code?
Everyone in IT should know the basics of programming. (Also you should have installed some Linux distribution on your laptop. Even if its your laptop, it increases your understanding of the complexities of managing a platform.)
Program something
Program a crappy little program, you will understand more about the challenges of the programmer.
Derek Sivers wrote a nice article about why you should learn programming. https://sivers.org/prog
For him learning to code means self reliance and basic understanding are the main reasons.
Also experience the joy of building you own computer. I helped my son when he built his gaming computer. I learned at least as much as he did.
What language to start with
Derek recommends to start with HTML and CSS. Well, yes, agree of if you are interested in programming web sites. But HTML is such an ugly programming language. It’s like staring programming with BASIC. Before you know you think GOTO is a great flexible feature. While it actually is kitsch. I would rather start with Python, php or Java.
Build something useful in a very short time. Make it ugly. It doesn’t matter. Improve it step by step. Or start something new.

I like exploring programming languages.

I recently played with php. Built a small website showing photo’s from google images using random keywords.
Using MAMP.
Then played with python, programming an interface between Kindle and Evernote. Used Pydev.
Did some Javascript and node-RED.
A lot of Rexx programming.
And Erlang. That’s a hard one if you are not familiar with functional programming languages.
I learned a ton. I am always amazed what you can learn FOR FREE on the Internet.

