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

generates a code of length 72 over Z7[X]/(X^2) who´s minimum homogenous weight is 425.

Homogenous weight enumerator: w(x)=1x^0+882x^425+192x^427+294x^432+72x^434+882x^439+24x^441+30x^448+24x^455

The gray image is a linear code over GF(7) with n=504, k=4 and d=425.
This code was found by Heurico 1.16 in 1.96 seconds.