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

generates a code of length 76 over Z7[X]/(X^2) who´s minimum homogenous weight is 434.

Homogenous weight enumerator: w(x)=1x^0+684x^434+420x^435+1848x^440+5316x^441+3066x^442+4326x^447+9618x^448+5166x^449+8568x^454+19554x^455+9240x^456+11886x^461+20046x^462+9282x^463+2184x^468+4350x^469+1638x^470+114x^476+126x^483+96x^490+42x^497+24x^504+36x^511+18x^518

The gray image is a linear code over GF(7) with n=532, k=6 and d=434.
This code was found by Heurico 1.16 in 6.78 seconds.