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

generates a code of length 94 over Z7[X]/(X^2) who´s minimum homogenous weight is 539.

Homogenous weight enumerator: w(x)=1x^0+132x^539+498x^546+462x^553+2058x^558+360x^560+12348x^565+294x^567+180x^574+84x^581+96x^588+84x^595+96x^602+24x^609+48x^616+6x^623+24x^637+6x^644+6x^651

The gray image is a linear code over GF(7) with n=658, k=5 and d=539.
This code was found by Heurico 1.16 in 0.592 seconds.