The generator matrix

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

generates a code of length 74 over Z7[X]/(X^2) who´s minimum homogenous weight is 434.

Homogenous weight enumerator: w(x)=1x^0+468x^434+1764x^435+630x^436+2646x^437+1050x^441+2394x^442+504x^443+882x^444+276x^448+504x^449+924x^450+2646x^451+570x^455+1512x^456+6x^462+24x^469+6x^476

The gray image is a linear code over GF(7) with n=518, k=5 and d=434.
This code was found by Heurico 1.16 in 0.183 seconds.