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

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+648x^392+294x^394+630x^396+420x^398+5664x^399+3108x^401+2016x^403+1680x^405+8904x^406+5376x^408+3402x^410+5670x^412+19716x^413+11676x^415+5208x^417+6636x^419+20592x^420+8358x^422+3150x^424+4014x^427+162x^434+126x^441+90x^448+42x^455+36x^462+24x^469+6x^476

The gray image is a linear code over GF(7) with n=483, k=6 and d=392.
This code was found by Heurico 1.16 in 5.97 seconds.