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

generates a code of length 62 over Z7[X]/(X^2) who´s minimum homogenous weight is 336.

Homogenous weight enumerator: w(x)=1x^0+456x^336+1296x^343+1626x^350+294x^354+1698x^357+5292x^361+2064x^364+31752x^368+1998x^371+63504x^375+1950x^378+2166x^385+1620x^392+942x^399+654x^406+282x^413+48x^420+6x^427

The gray image is a linear code over GF(7) with n=434, k=6 and d=336.
This code was found by Heurico 1.16 in 14 seconds.