The generator matrix

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

generates a code of length 71 over Z7[X]/(X^2) who´s minimum homogenous weight is 415.

Homogenous weight enumerator: w(x)=1x^0+2184x^415+462x^416+882x^419+174x^420+4284x^422+798x^423+294x^426+60x^427+2520x^429+252x^430+882x^433+36x^434+3360x^436+546x^437+66x^441+6x^448

The gray image is a linear code over GF(7) with n=497, k=5 and d=415.
This code was found by Heurico 1.16 in 79.3 seconds.