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

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+210x^427+516x^434+474x^441+342x^448+14406x^450+204x^455+174x^462+144x^469+96x^476+78x^483+60x^490+66x^497+30x^504+6x^525

The gray image is a linear code over GF(7) with n=525, k=5 and d=427.
This code was found by Heurico 1.16 in 0.415 seconds.