The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 0  7  0  7 21 21  0  7 21 14 14 14  0  7 21 14
 0  0  7 35 21 14 28 14  7 35  7 28 35 28  0 35

generates a code of length 16 over Z49 who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+54x^84+114x^91+2058x^96+96x^98+18x^105+60x^112

The gray image is a code over GF(7) with n=112, k=4 and d=84.
This code was found by Heurico 1.16 in 0.00175 seconds.