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  X  1  1  X  1  1  1  1  X  1  X  1  1  1  1  1
 0  X  0  0  0  0  0  0  X 3X  X  X  X 2X 6X 6X 5X 5X 2X 2X 2X 4X 2X 6X  X  X  0 2X 2X 3X 4X 4X 6X 6X 5X 6X  X  0  X  X 4X 2X 2X 3X 4X 6X 5X  X 2X  0  X  X  0 4X 2X  X 2X 3X 5X 2X 3X  X 4X
 0  0  X  0  0  X  X 4X 5X 4X 4X  X 5X 4X 3X  0  X 3X 2X  X 5X  0  X  0  0 3X 2X 6X 5X 2X 3X 4X  0  X 2X 5X 5X  X 5X 2X 4X 5X 4X 4X  X 5X  0 2X 5X 5X  X  0  X  0 6X 2X 4X  0 6X 5X  X 3X 3X
 0  0  0  X  0 5X 4X 3X 5X 3X 3X  X 6X 6X 2X  X 3X 5X 3X  0 4X 2X 6X 6X 2X 3X 4X  0 6X 6X 2X 4X 3X 6X 2X 2X 6X  X 2X 2X 2X 5X  0  X 3X 2X 5X  0 4X 5X 3X 5X 6X 3X 6X 4X 4X 3X 5X 2X 6X  X  0
 0  0  0  0  X 5X  X 2X 5X  0 5X 6X  X 4X 5X 5X 6X 6X 2X 3X 6X 6X 6X 3X 4X 6X  X 2X  0 2X 2X 5X 4X 2X 6X 4X 4X 5X 6X  0 2X 5X 3X 4X  0 6X 3X 2X 4X 2X 4X 5X  0 3X 6X 3X 2X 2X 4X 3X 6X 4X 4X

generates a code of length 63 over Z7[X]/(X^2) who´s minimum homogenous weight is 343.

Homogenous weight enumerator: w(x)=1x^0+654x^343+1278x^350+1584x^357+1176x^361+1974x^364+8820x^368+1914x^371+36456x^375+2190x^378+54390x^382+1980x^385+1836x^392+1446x^399+1086x^406+558x^413+228x^420+66x^427+12x^434

The gray image is a linear code over GF(7) with n=441, k=6 and d=343.
This code was found by Heurico 1.16 in 15.1 seconds.