Custom Field Polynomial in Reed-Solomon Encoder

I'm trying to create a Reed-Solomon encoder to generate ECC words for SMPTE 299M embedded audio.

The polynomial is x^6 + x^5 + x^3 + x^2 + x + 1.

These are the parameters I need:

Bits per symbol: 8

Symbols per codeword: 31

Check symbols per codeword: 6

Field polynomial: 111

When I choose the first three parameters, the Field Polynomial dropdown box starts at 285 and goes up from there.

Is there a way to get 111 in this field?