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

generates a code of length 75 over Z7[X]/(X^2) who´s minimum homogenous weight is 440.

Homogenous weight enumerator: w(x)=1x^0+2100x^440+78x^441+630x^442+1764x^443+4410x^447+150x^448+504x^449+588x^450+1050x^454+48x^455+924x^456+1764x^457+2730x^461+36x^462+6x^469+18x^476+6x^483

The gray image is a linear code over GF(7) with n=525, k=5 and d=440.
This code was found by Heurico 1.16 in 0.185 seconds.