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

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+252x^434+528x^441+456x^448+2058x^450+414x^455+12348x^457+150x^462+150x^469+126x^476+114x^483+54x^490+54x^497+48x^504+30x^511+18x^518+6x^525

The gray image is a linear code over GF(7) with n=532, k=5 and d=434.
This code was found by Heurico 1.16 in 0.42 seconds.