The generator matrix

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

generates a code of length 99 over Z7[X]/(X^2) who´s minimum homogenous weight is 575.

Homogenous weight enumerator: w(x)=1x^0+1092x^575+126x^576+420x^577+504x^578+1596x^579+2604x^580+3786x^581+6552x^582+714x^583+2814x^584+3192x^585+4830x^586+3906x^587+6030x^588+6888x^589+1008x^590+2982x^591+3528x^592+4200x^593+3738x^594+5760x^595+6342x^596+1218x^597+3318x^598+2520x^599+5124x^600+3318x^601+4464x^602+5544x^603+1050x^604+2814x^605+2604x^606+2772x^607+2898x^608+2892x^609+4452x^610+36x^616+12x^623

The gray image is a linear code over GF(7) with n=693, k=6 and d=575.
This code was found by Heurico 1.16 in 7.6 seconds.