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

generates a code of length 72 over Z7[X]/(X^2) who´s minimum homogenous weight is 406.

Homogenous weight enumerator: w(x)=1x^0+126x^406+252x^408+42x^411+294x^412+1566x^413+1974x^415+1176x^418+3108x^419+5574x^420+4494x^422+2394x^425+5376x^426+9936x^427+6258x^429+5922x^432+11676x^433+16746x^434+10122x^436+4872x^439+8358x^440+11070x^441+5712x^443+144x^448+174x^455+138x^462+42x^469+42x^476+60x^483

The gray image is a linear code over GF(7) with n=504, k=6 and d=406.
This code was found by Heurico 1.16 in 6.45 seconds.