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

generates a code of length 64 over Z7[X]/(X^2) who´s minimum homogenous weight is 364.

Homogenous weight enumerator: w(x)=1x^0+408x^364+432x^371+2568x^378+12678x^385+180x^392+132x^399+102x^406+108x^413+102x^420+66x^427+18x^434+12x^441

The gray image is a linear code over GF(7) with n=448, k=5 and d=364.
This code was found by Heurico 1.16 in 0.593 seconds.