The generator matrix

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

generates a code of length 74 over Z7[X]/(X^2) who´s minimum homogenous weight is 427.

Homogenous weight enumerator: w(x)=1x^0+2190x^427+1470x^428+336x^429+168x^430+336x^431+1176x^432+3570x^433+11106x^434+5124x^435+1302x^436+1176x^437+1218x^438+2478x^439+5376x^440+14268x^441+5586x^442+1932x^443+1260x^444+1260x^445+2100x^446+4998x^447+14040x^448+6384x^449+2352x^450+1512x^451+1302x^452+2478x^453+4578x^454+12204x^455+4074x^456+252x^457+12x^462+12x^469+12x^476+6x^483

The gray image is a linear code over GF(7) with n=518, k=6 and d=427.
This code was found by Heurico 1.16 in 5.57 seconds.