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

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

Homogenous weight enumerator: w(x)=1x^0+210x^350+570x^357+294x^360+426x^364+3528x^367+342x^371+10584x^374+222x^378+174x^385+144x^392+150x^399+66x^406+36x^413+42x^420+12x^427+6x^434

The gray image is a code over GF(7) with n=434, k=5 and d=350.
This code was found by Heurico 1.16 in 0.311 seconds.