This should give you a table in about 5 seconds. All the elements have equal number of 0 and 1 bits, although I don't really think that helps. Run time is about the same without this constraint.

Code:

// Generate table of 256 32-bit numbers such that no rotations
// of any 1 or 2 numbers XORed is equal to any third number.
#include <stdio.h>
#include <stdlib.h>
#include <time.h>
// Return a 32 bit random number with 16 zero bits and 16 ones.
unsigned int rnd() {
unsigned int r;
int c;
do {
r=rand()^rand()<<10^rand()<<19;
c=0; // bit count
for (int i=0; i<32; ++i)
c+=r>>i&1;
} while (c!=16);
return r;
}
int main() {
srand(time(0));
unsigned int t[257]={0}; // 0, then 256 random elements
for (int i=1; i<257; ++i) {
int good=1;
unsigned int c=0;
do {
c=rnd();
good=1;
for (int j=0; j<i && good; ++j) {
for (int m=0; m<32; ++m) {
unsigned int a=t[j]<<m|t[j]>>32-m;
for (int k=j+1; k<i; ++k) {
for (int n=0; n<32; ++n) {
unsigned int b=t[k]<<n|t[k]>>32-n;
if ((a^b)==c) good=0;
}
}
}
}
} while (!good);
t[i]=c;
printf(" 0x%08X, // %d\n", c, i-1);
}
return 0;
}