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

generates a code of length 75 over Z7[X]/(X^2) who´s minimum homogenous weight is 413.

Homogenous weight enumerator: w(x)=1x^0+666x^413+1296x^420+1512x^427+1872x^434+1656x^441+1902x^448+100842x^450+1830x^455+1872x^462+1674x^469+1038x^476+690x^483+540x^490+210x^497+36x^504+6x^511+6x^525

The gray image is a linear code over GF(7) with n=525, k=6 and d=413.
This code was found by Heurico 1.16 in 21.4 seconds.