In the Legacy Toolchain
Load the legacy text encodings you’ll need with fontenc
, then fill in any missing characters with \newunicodechar
.
\documentclass{article}
\usepackage[LGR, T1]{fontenc}
\usepackage{textcomp}
\usepackage[utf8]{inputenc} % The default since 2018
\usepackage{lmodern, newunicodechar}
\usepackage[cache=false]{minted}
% To fit within the width allowed on TeX.SX:
\usepackage[paperwidth=10cm]{geometry}
% ϕ(U+03D5) is the math symbol with a vertical stroke. It is in OML.
\renewcommand\textphisymbol{\ensuremath{\mathtt{\phi}}}
\newunicodechar{ⁿ}{\textsuperscript{n}}
% 𝚽(U+1D6DF) is present in certain font packages, but there is no typewriter
% bold upright font face of either cmtt or lmtt in LGR or OT1. Should fall
% back to normal weight.
\newunicodechar{𝚽}{{\usefont{LGR}{\ttdefault}{bf}{n}\selectfont\symbol{"46}}}
% Should be the mathematical symbol, rather than the Greek lowercase letter:
\renewcommand\texttheta{\ensuremath{\mathtt{\theta}}}
\begin{document}
\inputminted{julia}{polynomial-regression.ji}
\end{document}
The following is cropped for display here:

Unfortunately, the alphabeta
and babel
packages appear to be incompatible with minted
, but you can load textgreek
as an alternative to redefining \texttheta
, etc.
You’ll likely want to be more consistent than I was about whether you use upright or slanted Greek letters. The default font family doesn’t have a bold typewriter Φ, so in this sample it fell back to regular weight. You can substitute the glyph you prefer from any Type 1 font of your choice. The Φ glyph is in the legacy LGR, OML and OT1 encodings, and in several fonts with non-standard encodings as well.
In the Modern Toolchain
Although you tagged the question with pdftex
, the easiest and best solution by far is to load fontspec
and a monospaced font that contains all the symbols you use, such as the one in your editor. Then compile with LuaLaTeX or XeLaTeX.
The following patches the CM Unicode fonts with a few Greek math symbols from Latin Modern Math:
\documentclass{article}
\usepackage{unicode-math}
\usepackage[cache=false]{minted}
\usepackage{newunicodechar}
% To fit within the width allowed on TeX.SX:
\usepackage[paperwidth=9cm]{geometry}
\defaultfontfeatures{Scale = MatchLowercase}
\setmainfont{CMU Serif}[Scale = 1.0]
\setsansfont{CMU Sans Serif}
\setmonofont{CMU Typewriter Text}
\setmathfont{Latin Modern Math}
% Although you could select a font that contains all the symbols your
% source uses, I’ll fall back here on redefining the handful that are
% missing.
\newfontface\mathsymbolfont{Latin Modern Math}
\newunicodechar{ϕ}{{\mathsymbolfont\mitphi}}
\newunicodechar{𝚽}{{\mathsymbolfont\mbfPhi}}
\begin{document}
\inputminted{julia}{polynomial-regression.ji}
\end{document}

This has a number of advantages, including that you can copy the source from the PDF and paste into an editor.
An alternative to ɸ would be to redefine ϕ (U+03D5, Greek Phi Symbol) as ɸ (U+0278, Latin Small Letter Phi), which CMU Typewriter Text does contain. Or you can instead make other Greek letters, such as θ, slanted for consistency.