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

generates a code of length 96 over Z7[X]/(X^2) who´s minimum homogenous weight is 553.

Homogenous weight enumerator: w(x)=1x^0+342x^553+630x^554+420x^556+420x^557+630x^558+1008x^559+1848x^560+4746x^561+2604x^563+1638x^564+2226x^565+2310x^566+2904x^567+7896x^568+2562x^570+3150x^571+2772x^572+3192x^573+3630x^574+10332x^575+3360x^577+5628x^578+5838x^579+5292x^580+5250x^581+13776x^582+3948x^584+3570x^585+2940x^586+2604x^587+2364x^588+5838x^589+1512x^591+90x^595+126x^602+78x^609+30x^616+60x^623+42x^630+6x^637+24x^644+6x^651+6x^658

The gray image is a linear code over GF(7) with n=672, k=6 and d=553.
This code was found by Heurico 1.16 in 8.63 seconds.