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

generates a code of length 64 over Z49 who´s minimum homogenous weight is 343.

Homogenous weight enumerator: w(x)=1x^0+78x^343+768x^350+1446x^357+588x^362+1656x^364+3528x^369+1734x^371+16758x^376+1938x^378+39984x^383+2052x^385+39984x^390+2040x^392+1956x^399+1416x^406+966x^413+522x^420+204x^427+18x^434+12x^441

The gray image is a code over GF(7) with n=448, k=6 and d=343.
This code was found by Heurico 1.16 in 14.6 seconds.