The generator matrix

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

generates a code of length 72 over Z7[X]/(X^2) who´s minimum homogenous weight is 421.

Homogenous weight enumerator: w(x)=1x^0+1638x^421+1008x^422+882x^425+198x^427+4032x^428+1344x^429+294x^432+90x^434+1722x^435+756x^436+882x^439+2898x^442+1008x^443+12x^448+36x^455+6x^469

The gray image is a linear code over GF(7) with n=504, k=5 and d=421.
This code was found by Heurico 1.16 in 99.8 seconds.