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

generates a code of length 74 over Z7[X]/(X^2) who´s minimum homogenous weight is 420.

Homogenous weight enumerator: w(x)=1x^0+342x^420+42x^421+126x^423+336x^424+588x^426+2460x^427+1428x^428+2226x^430+2982x^431+2184x^433+4170x^434+2268x^435+4914x^437+5502x^438+3150x^440+8064x^441+3612x^442+11802x^444+11634x^445+5376x^447+10176x^448+4746x^449+9744x^451+8358x^452+3108x^454+5502x^455+2310x^456+156x^462+126x^469+66x^476+78x^483+12x^490+36x^497+6x^504+18x^511

The gray image is a linear code over GF(7) with n=518, k=6 and d=420.
This code was found by Heurico 1.16 in 6.61 seconds.