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

generates a code of length 89 over Z7[X]/(X^2) who´s minimum homogenous weight is 511.

Homogenous weight enumerator: w(x)=1x^0+396x^511+1218x^516+3066x^517+4518x^518+4116x^523+6846x^524+7896x^525+6510x^530+9576x^531+10458x^532+10920x^537+15960x^538+14970x^539+6048x^544+7770x^545+6960x^546+144x^553+48x^560+60x^567+12x^574+42x^581+36x^588+42x^595+12x^602+24x^609

The gray image is a linear code over GF(7) with n=623, k=6 and d=511.
This code was found by Heurico 1.16 in 7.95 seconds.