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

generates a code of length 71 over Z7[X]/(X^2) who´s minimum homogenous weight is 399.

Homogenous weight enumerator: w(x)=1x^0+66x^399+84x^400+42x^402+42x^405+702x^406+1470x^407+840x^408+840x^409+1260x^412+3540x^413+4872x^414+1554x^415+2562x^416+2142x^419+5742x^420+9240x^421+3528x^422+3024x^423+6174x^426+12054x^427+16170x^428+5502x^429+5334x^430+4788x^433+8508x^434+11382x^435+2982x^436+2604x^437+186x^441+156x^448+78x^455+54x^462+66x^469+30x^476+12x^483+18x^490

The gray image is a linear code over GF(7) with n=497, k=6 and d=399.
This code was found by Heurico 1.16 in 6.34 seconds.