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  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  7  1 21  1  1  1  1  1  1  1  1  1  1  7  1  1 35  1  1
 0  1  1 31 16 48  4 19  0 36 31 16 48  4 19  1 19 16 48 36  4  1  0 31 38 36  7 26  9 14 26  3  5 23 16 40  3 21  3 21 40  3 28  1 14  1 28 29  6 46 20 29 11 21 36 30  1 14 20  1 29 43
 0  0 35  0 35  7 35  7 42 14  7 42  0  0 42 14 21 28 14 21 42 14 21  7 35 21 21 42  7 35 21 35 28 14  7  7 21 42 35  0 14  0 35  7 28  7 28  7 21 35 42 42 14 14  0 21 35  0 35  7 42 14
 0  0  0  7 28 28 21 42  0 42  7 42 35 28 21 21 42 21 35 35 14  0 42  0 35 21  7 35 21  7 14 28 14 28 42  0  7  7  0 35 14 14 21 35 35  0 28 14 28  7  0 42 21 14  0  7 42 21 35 42 35  7

generates a code of length 62 over Z49 who´s minimum homogenous weight is 350.

Homogenous weight enumerator: w(x)=1x^0+258x^350+126x^351+294x^352+378x^353+1932x^356+1242x^357+2184x^358+3150x^359+1722x^360+4074x^363+2574x^364+5040x^365+5250x^366+3150x^367+8820x^370+6120x^371+11676x^372+11802x^373+5544x^374+11802x^377+6030x^378+9786x^379+8316x^380+3612x^381+2184x^384+156x^385+132x^392+114x^399+72x^406+42x^413+48x^420+18x^427

The gray image is a code over GF(7) with n=434, k=6 and d=350.
This code was found by Heurico 1.16 in 5.65 seconds.