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

generates a code of length 97 over Z7[X]/(X^2) who´s minimum homogenous weight is 563.

Homogenous weight enumerator: w(x)=1x^0+840x^563+168x^564+336x^565+882x^566+2040x^567+1092x^568+5880x^569+5292x^570+1260x^571+2016x^572+3276x^573+5178x^574+1512x^575+8274x^576+5502x^577+2394x^578+3024x^579+3990x^580+5226x^581+1134x^582+7434x^583+4704x^584+2520x^585+2730x^586+3360x^587+4722x^588+1176x^589+7350x^590+5166x^591+1890x^592+2184x^593+2898x^594+3696x^595+1260x^596+3990x^597+3192x^598+30x^602+24x^609+6x^616

The gray image is a linear code over GF(7) with n=679, k=6 and d=563.
This code was found by Heurico 1.16 in 7.87 seconds.