The generator matrix

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

generates a code of length 75 over Z7[X]/(X^2) who´s minimum homogenous weight is 434.

Homogenous weight enumerator: w(x)=1x^0+1746x^434+3990x^435+588x^436+1512x^437+2604x^438+1764x^439+1050x^440+4896x^441+10164x^442+1806x^443+3024x^444+4326x^445+1974x^446+1176x^447+6186x^448+12642x^449+2856x^450+3528x^451+4704x^452+2520x^453+966x^454+5442x^455+12348x^456+2982x^457+4284x^458+4830x^459+1974x^460+924x^461+4626x^462+6132x^463+36x^469+24x^476+24x^483

The gray image is a linear code over GF(7) with n=525, k=6 and d=434.
This code was found by Heurico 1.16 in 7.57 seconds.