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

generates a code of length 76 over Z7[X]/(X^2) who´s minimum homogenous weight is 447.

Homogenous weight enumerator: w(x)=1x^0+2520x^447+762x^448+1764x^449+1050x^450+2688x^454+612x^455+588x^456+252x^457+1176x^461+960x^462+1764x^463+756x^464+1848x^468+24x^469+12x^476+24x^483+6x^490

The gray image is a linear code over GF(7) with n=532, k=5 and d=447.
This code was found by Heurico 1.16 in 46.2 seconds.