The generator matrix

 1  0  1  1  1  1  1  1  1  1  1  1  1  1  1  0  1  1  1  1  1  0  1  1  1  1  1  1  1  1  1  1  1  1  7  1  1  1  1  1  1  7 28  7  1  1  1  1  1  1  1  1  1  1  1  1  1 42 14  1 14 42  1  1 42  1  1  1  1  1 42  1  1  1 21  1  1 14  1  1  1  1  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  4 19  1 19 16 48 36  4  1  0 31 36 26 38  7  6 46  9 29  7 38  1  9 43  6 21 40  9  1  1  1 12 20 44 20 32 15 44 29 29  3  4 10 36  1  1 11  1  1  7 29  1 19 38 46 46 29  1  8 40 13  1  9 35  1 41 10 21 25 16 34 11 45  7 44 14 20  6 16 18 13 33  4
 0  0 35  0 35  7 35  7 42 14  7 42  0  0 42 14 21 28 14 21 42 14 21  0 14 42 35 28 21 14 28  7 14 14 35 21 42  7 35 35 21  7 42 28 35 42 14 42 42  0  0  7 21 14  7  7  7 35 42  7 21 21 14 42 42  7 28 35 28 42 28  0 28 42 35  7 28 42 42 28 42 35 35 21  7 35  0 35 35 35 21  7 14 14 42 14
 0  0  0  7 28 28 21 42  0 42  7 42 35 28 21 21 42 21 35 35 14  0 42 14  7 35 35 28 28 21  0 14 14 21 42  7 42  0  7 42 21 35 28 21 28  0 28 42 35 42  7  7 21 35 28  0 21  7 14  7 42 35 21 21 35 35  0  7 35 28  0 35 14 35 35 28 42  7  7 21 28 35 21  7 14  0  7 42 21 28 42 42  7  7 14 28

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

Homogenous weight enumerator: w(x)=1x^0+342x^553+630x^554+420x^556+420x^557+630x^558+1008x^559+1848x^560+4746x^561+2604x^563+1638x^564+2226x^565+2310x^566+2904x^567+7896x^568+2562x^570+3150x^571+2772x^572+3192x^573+3630x^574+10332x^575+3360x^577+5628x^578+5838x^579+5292x^580+5250x^581+13776x^582+3948x^584+3570x^585+2940x^586+2604x^587+2364x^588+5838x^589+1512x^591+90x^595+126x^602+78x^609+30x^616+60x^623+42x^630+6x^637+24x^644+6x^651+6x^658

The gray image is a code over GF(7) with n=672, k=6 and d=553.
This code was found by Heurico 1.16 in 9.31 seconds.