The generator matrix

 1  0  1  1  1  1  1  1  1  1  1  0  1  1  1  1  7  1  1  7  1  1  1  1  1  1 28 28  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  1  1 31 16 48  4 19  0 36 31  1 16 19  7 36  1  9 29  1 23 38  7 14 23 29  1  1 15  9 14 38 10  3  3 10 48  4  6 46 26 46  6 26 20 33  5 32 20 11 41  5 32
 0  0 35 21 42  7 14 21  7 28 14  7 35  0 28 14 35  7 21 42  0 42 42 14 21  7 14 28  0 28 21  7  0  7 21 42 42 28 28  0 14 42 21  7 35 35 42 35 14 21  0 28  7

generates a code of length 53 over Z49 who´s minimum homogenous weight is 308.

Homogenous weight enumerator: w(x)=1x^0+60x^308+2520x^310+2646x^311+1050x^312+108x^315+2016x^317+882x^318+252x^319+114x^322+3696x^324+2646x^325+756x^326+48x^329+6x^336+6x^343

The gray image is a code over GF(7) with n=371, k=5 and d=308.
This code was found by Heurico 1.16 in 23.9 seconds.