The generator matrix

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

generates a code of length 69 over Z7[X]/(X^2) who´s minimum homogenous weight is 404.

Homogenous weight enumerator: w(x)=1x^0+1806x^404+420x^405+714x^406+1764x^407+3150x^411+630x^412+696x^413+588x^414+1218x^418+1008x^419+942x^420+1764x^421+2058x^425+6x^427+12x^434+24x^441+6x^448

The gray image is a linear code over GF(7) with n=483, k=5 and d=404.
This code was found by Heurico 1.16 in 0.339 seconds.