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

generates a code of length 69 over Z7[X]/(X^2) who´s minimum homogenous weight is 392.

Homogenous weight enumerator: w(x)=1x^0+258x^392+558x^399+402x^406+2058x^408+324x^413+12348x^415+228x^420+180x^427+120x^434+132x^441+84x^448+30x^455+60x^462+18x^469+6x^476

The gray image is a linear code over GF(7) with n=483, k=5 and d=392.
This code was found by Heurico 1.16 in 0.368 seconds.