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  7  1  7  1 21  1  1  1  1  1  1  1  1  1  1  1  1  1  1 14  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 36 48 26  1  4  1  0  1 31  1  7 40 26 38  7 26 12 36 46 38  9  6 29  9  1  9 11 10 15  7 21 23 46 37 25 20  0
 0  0 35  0 35  7 35  7 42 14  7 42  0  0 42 14 21 28 21 14 28  7  7 28 14  7 14 42 21  7 35  0 35 21  0  0 14 14 21 42 42  7 28  7  7 35 14 21 42 35  7 21 42 21  7
 0  0  0  7 28 28 21 42  0 42  7 42 35 28 21 21 42 21 35 35 35 21  0 28 35 35 28 28 42 35 14 14  7 21  7 28  7 21  7 28 35 21  7  7 28 21 21 28 21  7 42 28 28  7  7

generates a code of length 55 over Z49 who´s minimum homogenous weight is 308.

Homogenous weight enumerator: w(x)=1x^0+246x^308+84x^309+546x^310+378x^314+2106x^315+2352x^316+4578x^317+1806x^321+4362x^322+4788x^323+7686x^324+5544x^328+12318x^329+11844x^330+18102x^331+6678x^335+11514x^336+9744x^337+12306x^338+204x^343+198x^350+102x^357+96x^364+54x^371+6x^378+6x^385

The gray image is a code over GF(7) with n=385, k=6 and d=308.
This code was found by Heurico 1.16 in 4.97 seconds.