The generator matrix

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

generates a code of length 73 over Z7[X]/(X^2) who´s minimum homogenous weight is 421.

Homogenous weight enumerator: w(x)=1x^0+2394x^421+966x^422+42x^423+252x^424+210x^425+2478x^426+3612x^427+11088x^428+3234x^429+1134x^430+1848x^431+546x^432+4494x^433+5580x^434+15330x^435+3612x^436+1134x^437+1722x^438+630x^439+4746x^440+4968x^441+13818x^442+3906x^443+1806x^444+2352x^445+672x^446+4746x^447+4668x^448+12936x^449+2688x^450+6x^455+18x^462+12x^469

The gray image is a linear code over GF(7) with n=511, k=6 and d=421.
This code was found by Heurico 1.16 in 5.42 seconds.