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

generates a code of length 68 over Z7[X]/(X^2) who´s minimum homogenous weight is 385.

Homogenous weight enumerator: w(x)=1x^0+360x^385+210x^387+3402x^391+1626x^392+1554x^393+798x^394+7476x^398+2958x^399+4158x^400+2520x^401+15666x^405+3960x^406+11718x^407+6132x^408+23184x^412+4914x^413+11382x^414+4746x^415+7896x^419+2502x^420+162x^427+126x^434+60x^441+72x^448+30x^455+24x^462+12x^469

The gray image is a linear code over GF(7) with n=476, k=6 and d=385.
This code was found by Heurico 1.16 in 5.97 seconds.