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

generates a code of length 93 over Z7[X]/(X^2) who´s minimum homogenous weight is 542.

Homogenous weight enumerator: w(x)=1x^0+1302x^542+4536x^543+5754x^544+1806x^545+912x^546+4158x^549+9408x^550+9282x^551+3234x^552+1878x^553+4914x^556+10500x^557+9534x^558+3612x^559+1884x^560+4242x^563+9072x^564+8274x^565+2310x^566+1818x^567+3906x^570+7644x^571+6258x^572+1386x^573+18x^588+6x^595

The gray image is a linear code over GF(7) with n=651, k=6 and d=542.
This code was found by Heurico 1.16 in 10.5 seconds.