The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 0  7  0  0  7  7 28 14 21  0  7 21 21 21 35  0
 0  0  7  0 35 28 21 35 42 21 21 21 35 35 28  7
 0  0  0  7 35  7 14 42 42 28  7  0 14 42 42 35

generates a code of length 16 over Z49 who´s minimum homogenous weight is 77.

Homogenous weight enumerator: w(x)=1x^0+120x^77+450x^84+444x^91+14406x^96+528x^98+684x^105+174x^112

The gray image is a code over GF(7) with n=112, k=5 and d=77.
This code was found by Heurico 1.16 in 0.0523 seconds.