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

generates a code of length 63 over Z7[X]/(X^2) who´s minimum homogenous weight is 357.

Homogenous weight enumerator: w(x)=1x^0+330x^357+480x^364+402x^371+2058x^372+378x^378+12348x^379+246x^385+174x^392+126x^399+78x^406+78x^413+48x^420+42x^427+12x^434+6x^441

The gray image is a linear code over GF(7) with n=441, k=5 and d=357.
This code was found by Heurico 1.16 in 0.315 seconds.