The generator matrix

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

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+180x^504+522x^511+438x^518+342x^525+14406x^528+258x^532+156x^539+156x^546+126x^553+60x^560+48x^567+36x^574+24x^581+12x^588+30x^595+6x^602+6x^616

The gray image is a linear code over GF(7) with n=616, k=5 and d=504.
This code was found by Heurico 1.16 in 0.53 seconds.