The generator matrix

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

generates a code of length 96 over Z49 who´s minimum homogenous weight is 553.

Homogenous weight enumerator: w(x)=1x^0+240x^553+528x^560+462x^567+324x^574+14406x^576+210x^581+180x^588+144x^595+84x^602+54x^609+48x^616+48x^623+30x^630+6x^637+12x^644+12x^651+12x^658+6x^672

The gray image is a code over GF(7) with n=672, k=5 and d=553.
This code was found by Heurico 1.16 in 0.599 seconds.