For cake: Preheat oven to 350°F. Butter an 8x4-inch loaf pan.
In a bowl, sift together flour, salt, allspice, baking powder, and baking soda.
In another bowl, combine the sugar, oil, and vanilla. Beat in eggs, once at a time. Add flour mixture, a little at a time, and mix until smooth. Add the beets, raisins, and walnuts. Pour mixture into prepared pan. Bake for 1 hour, or until a toothpick inserted into the center comes out clean. Turn cake out on a cooling rack.
For frosting: In a bowl, beat together butter, cream cheese, and vanilla. Gradually beat in sugar. If mixture is too thick, add a small amount of milk.
Spread frosting on cooled cake.