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

generates a code of length 73 over Z7[X]/(X^2) who´s minimum homogenous weight is 413.

Homogenous weight enumerator: w(x)=1x^0+120x^413+492x^420+474x^427+2058x^432+330x^434+12348x^439+246x^441+234x^448+114x^455+102x^462+120x^469+66x^476+54x^483+30x^490+6x^497+12x^504

The gray image is a linear code over GF(7) with n=511, k=5 and d=413.
This code was found by Heurico 1.16 in 0.4 seconds.