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

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+162x^413+966x^419+2862x^420+840x^423+5922x^426+8832x^427+1890x^430+8190x^433+12942x^434+6048x^437+17556x^440+22488x^441+5628x^444+10584x^447+12312x^448+120x^455+72x^462+60x^469+30x^476+30x^483+78x^490+30x^497+6x^504

The gray image is a linear code over GF(7) with n=511, k=6 and d=413.
This code was found by Heurico 1.16 in 6.41 seconds.