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

generates a code of length 76 over Z7[X]/(X^2) who´s minimum homogenous weight is 413.

Homogenous weight enumerator: w(x)=1x^0+180x^413+666x^420+1254x^427+1632x^434+1896x^441+2058x^444+1848x^448+24696x^451+1866x^455+74088x^458+1752x^462+1674x^469+1332x^476+1242x^483+762x^490+456x^497+174x^504+54x^511+12x^518+6x^525

The gray image is a linear code over GF(7) with n=532, k=6 and d=413.
This code was found by Heurico 1.16 in 17.3 seconds.