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

generates a code of length 88 over Z7[X]/(X^2) who´s minimum homogenous weight is 504.

Homogenous weight enumerator: w(x)=1x^0+282x^504+378x^505+1974x^510+2496x^511+3528x^512+5922x^517+4620x^518+7518x^519+10080x^524+7566x^525+10416x^526+15918x^531+10230x^532+14700x^533+9324x^538+5502x^539+6678x^540+144x^546+102x^553+60x^560+78x^567+42x^574+48x^581+30x^588+12x^595

The gray image is a linear code over GF(7) with n=616, k=6 and d=504.
This code was found by Heurico 1.16 in 7.88 seconds.