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

generates a code of length 75 over Z7[X]/(X^2) who´s minimum homogenous weight is 427.

Homogenous weight enumerator: w(x)=1x^0+438x^427+294x^428+84x^429+420x^430+3252x^434+1470x^435+2394x^436+4872x^437+4614x^441+2520x^442+4662x^443+7560x^444+8106x^448+3612x^449+11970x^450+17976x^451+9606x^455+4620x^456+9702x^457+12390x^458+4680x^462+1890x^463+114x^469+186x^476+78x^483+54x^490+42x^497+24x^504+18x^511

The gray image is a linear code over GF(7) with n=525, k=6 and d=427.
This code was found by Heurico 1.16 in 6.71 seconds.