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

generates a code of length 73 over Z7[X]/(X^2) who´s minimum homogenous weight is 399.

Homogenous weight enumerator: w(x)=1x^0+336x^399+1128x^406+1494x^413+1800x^420+1698x^427+1902x^434+100842x^438+2010x^441+1752x^448+1602x^455+1302x^462+948x^469+576x^476+192x^483+36x^490+24x^497+6x^511

The gray image is a linear code over GF(7) with n=511, k=6 and d=399.
This code was found by Heurico 1.16 in 17 seconds.