The generator matrix

 1  0  1  1  1  1  1  1  1  1  1  0  1  1  1  1  1  1  1  1  1  1  1  1  1  1  7  1  1  7  1  1  1  1  1  1  1  1  1  1 28  1  1  1  1  1  1  1  1 28  0  1  1  1  1 21  1  1 21  1  1  1 28  1  1  1  1  1  7  1  1  1 35  1  1 35  1  1  1  1  1  1  1  1
 0  1  1 31 16 48  4 19  0 36 31  1 16 19 48  4 36  7 38 26  9  9  6  6 44 46  1 20 46  1 32 32  7 43 38 26 21 43 45 33  1 21 22 45 33 23 42 22 11  1  1 23 37 20 13  1 13 34  1  7 21 42  1 34 16  9 44 48  1 42 20 44  1 14 34  1 14 37 36  1 29 22  1 29
 0  0 35 21 42  7 14 21  7 28 14  7 35  0  0 28 42 14 42 28  7 21 35 21 14  0 14 28 42 42  7 35 42 21 28 35 21  0  7 14 28 35  7  0 42 21 28 14 21 14 21  7 14 35 14 21 28 14 42 35  0  7 35 42  0 35 42 21  0 42  0 28 28 21  7  7 28  0  7 28 35  0 21 14

generates a code of length 84 over Z49 who´s minimum homogenous weight is 496.

Homogenous weight enumerator: w(x)=1x^0+5040x^496+1002x^497+4788x^503+438x^504+2058x^510+918x^511+2520x^517+18x^518+6x^525+6x^539+12x^546

The gray image is a code over GF(7) with n=588, k=5 and d=496.
This code was found by Heurico 1.16 in 88.5 seconds.