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

generates a code of length 59 over Z7[X]/(X^2) who´s minimum homogenous weight is 336.

Homogenous weight enumerator: w(x)=1x^0+276x^336+654x^343+2058x^348+564x^350+12348x^355+510x^357+102x^364+12x^371+18x^378+18x^385+66x^392+126x^399+48x^406+6x^413

The gray image is a linear code over GF(7) with n=413, k=5 and d=336.
This code was found by Heurico 1.16 in 23.4 seconds.