Steam alone will not clean dirty grout on wall tiles, not matter how powerful the steam cleaner is!
Try mixing 1 part chlorine bleach, with 5 parts water, spray on tiles, and then use a grout brush or tooth brush and scrub.
Sponge down two or three times with plain water after scrubbing to get rid of the cleaning solution.
Don`t use this method of cleaning on coloured grout, and be careful not to work with bleach near ammonia based products.
Also wear goggles and glove and old clothes!
There are other methods & chemicals, but test this method of cleaning first on a small area, and wait 24 hours to see results.