The generator matrix

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

generates a code of length 64 over Z7[X]/(X^2) who´s minimum homogenous weight is 373.

Homogenous weight enumerator: w(x)=1x^0+1218x^373+840x^375+1764x^377+174x^378+3402x^380+1260x^382+588x^384+90x^385+1302x^387+2016x^389+1764x^391+24x^392+2310x^394+18x^399+24x^406+12x^413

The gray image is a linear code over GF(7) with n=448, k=5 and d=373.
This code was found by Heurico 1.16 in 23.1 seconds.