Converting colored output into html
The answer to this question is probably what you want.
It links to these tools, which do the conversion you're looking for:
Perl package HTML::FromANSI
aha, a C-language program (github repo)
Or just a shell script
https://github.com/pixelb/scripts/blob/master/scripts/ansi2html.sh
More details of this script http://pablomarin-garcia.blogspot.com/2011/04/converting-ansi-to-html-how-to-convert.html
You can try vim with AnsiEsc.vim plugin to view ANSI colors through escape codes, then redirect to standard output to vim - (make sure you've activated :syntax on). Then convert the file to HTML by vim command: :TOhtml. The generated HTML file should have coloured output.
To convert source code non-interactively into html, try the following command:
vim -E -s -c "let g:html_no_progress=1" -c "syntax on" -c "set ft=c" -c "runtime syntax/2html.vim" -cwqa myfile.c
Source: :help g:html_no_progress (part of :help TOhtml).
Note: You can use - instead of the myfile.c, to convert code from standard input.