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

generates a code of length 68 over Z49 who´s minimum homogenous weight is 385.

Homogenous weight enumerator: w(x)=1x^0+180x^385+522x^392+444x^399+2058x^402+372x^406+12348x^409+246x^413+210x^420+96x^427+114x^434+84x^441+24x^448+72x^455+30x^462+6x^469

The gray image is a code over GF(7) with n=476, k=5 and d=385.
This code was found by Heurico 1.16 in 0.354 seconds.