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

generates a code of length 95 over Z7[X]/(X^2) who´s minimum homogenous weight is 546.

Homogenous weight enumerator: w(x)=1x^0+270x^546+84x^547+294x^549+1008x^551+1218x^552+3564x^553+1344x^554+2142x^556+2268x^558+4284x^559+6984x^560+2310x^561+2436x^563+2562x^565+6300x^566+10578x^567+3570x^568+3654x^570+3906x^572+10836x^573+15522x^574+4830x^575+4158x^577+3318x^579+6174x^580+8172x^581+2268x^582+1722x^584+1344x^586+132x^588+126x^595+108x^602+60x^609+30x^616+30x^623+12x^630+12x^637+6x^644+12x^651

The gray image is a linear code over GF(7) with n=665, k=6 and d=546.
This code was found by Heurico 1.16 in 8.55 seconds.