The generator matrix

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

generates a code of length 59 over Z7[X]/(X^2) who´s minimum homogenous weight is 329.

Homogenous weight enumerator: w(x)=1x^0+54x^329+84x^333+1050x^335+1188x^336+336x^337+2394x^340+5628x^342+2442x^343+2520x^344+4662x^347+8568x^349+3456x^350+10416x^351+11970x^354+17346x^356+6042x^357+15540x^358+9702x^361+10626x^363+3090x^364+144x^371+168x^378+84x^385+102x^392+18x^399+12x^406+6x^413

The gray image is a linear code over GF(7) with n=413, k=6 and d=329.
This code was found by Heurico 1.16 in 5.05 seconds.