I have not grown this
mushroom, but I did a little looking around the internet.
Believe it or not, the "enoki mushroom" often found in grocery stores and restaurants, also called the "enokitake," is a cultivated form of Flammulina velutipes. It looks nothing like the wild mushroom, however; it is pale, long-stemmed, and tiny-capped (see the illustration).
https://www.mushroomexpert.com/flammulina_velutipes.html
Now we know the Latin name (Flammulina velutipes), a bit more looking shows this...
Enokitake, aka "The Velvet Foot" is a surprisingly flavorful mushroom that is quite popular in Japan. It grows well on hardwood sawdust/chips/bran, producing delightfully long stems and small caps under elevated CO2 levels. https://fungi.com/products/flammulina-velutipes-culture
And
Velvet Foot Mushroom aka Enokitake (Flamulina velutipes)
Fruits under cool conditions. In Asia gown in jars under low light and high CO2 to produce long thin stems and minute caps. Very different appearance in nature. Grow on sawdust, paper and cardboard. https://www.namyco.org/common_cultivars.php
So, I didn't find anything about growing in wheat
straw. Maybe you could use paper or
cardboard instead?
Perhaps someone more knowledgeable will come along to help you. Good luck!