The generator matrix

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

generates a code of length 72 over Z7[X]/(X^2) who´s minimum homogenous weight is 415.

Homogenous weight enumerator: w(x)=1x^0+1512x^415+1596x^416+504x^418+882x^419+1278x^420+6090x^421+7518x^422+5124x^423+2772x^425+2226x^426+2544x^427+8610x^428+9912x^429+5250x^430+3234x^432+2310x^433+2148x^434+8610x^435+9786x^436+6552x^437+3780x^439+2814x^440+2544x^441+7560x^442+8316x^443+4116x^444+24x^448+30x^455+6x^469

The gray image is a linear code over GF(7) with n=504, k=6 and d=415.
This code was found by Heurico 1.16 in 5.38 seconds.