The generator matrix

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

generates a code of length 94 over Z7[X]/(X^2) who´s minimum homogenous weight is 548.

Homogenous weight enumerator: w(x)=1x^0+1092x^548+5712x^549+4452x^550+2520x^551+588x^552+42x^553+2436x^555+11592x^556+8526x^557+4662x^558+1176x^559+96x^560+3234x^562+13146x^563+7938x^564+3948x^565+1176x^566+150x^567+3024x^569+11634x^570+6594x^571+3318x^572+1176x^573+36x^574+2562x^576+9366x^577+5418x^578+2016x^579+12x^595+6x^602

The gray image is a linear code over GF(7) with n=658, k=6 and d=548.
This code was found by Heurico 1.16 in 65.1 seconds.