Hey, apologies for the late reply. Here is the palette I used.
It's a very slightly modified Pico-8 colour palette (I think all I did was basically just dulled down the brown)
And here are the colour codes to match:
#000000, #1d2b53, #7e2553, #008751,
#a46422, #5f574f, #83769c, #c2c3c7,
#ffa300, #ffec27, #00e436, #29adff,
#fff1e8, #ff77a8, #ffccaa, #ff004d