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

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

Homogenous weight enumerator: w(x)=1x^0+192x^308+558x^315+450x^322+252x^329+14406x^330+330x^336+198x^343+144x^350+126x^357+72x^364+42x^371+30x^378+6x^385

The gray image is a code over GF(7) with n=385, k=5 and d=308.
This code was found by Heurico 1.16 in 0.267 seconds.