The generator matrix

 1  0  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 0  1  1 31 16 48  4 19  0 36 31 16 48  0  4  7
 0  0 35  0 35  7 35  7 42 14  7 42  0 28  0 35
 0  0  0  7 28 28 21 42  0 42  7 42 35 35 28 28

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

Homogenous weight enumerator: w(x)=1x^0+126x^77+168x^79+1908x^84+1260x^86+4116x^90+18072x^91+5208x^93+24696x^97+53496x^98+7770x^100+642x^105+186x^112

The gray image is a code over GF(7) with n=112, k=6 and d=77.
This code was found by Heurico 1.16 in 0.989 seconds.