The generator matrix

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

generates a code of length 85 over Z7[X]/(X^2) who´s minimum homogenous weight is 494.

Homogenous weight enumerator: w(x)=1x^0+2940x^494+4536x^495+630x^496+312x^497+1218x^498+1176x^499+1596x^500+11424x^501+8316x^502+1890x^503+1584x^504+2520x^505+1890x^506+1764x^507+11802x^508+9954x^509+1470x^510+1020x^511+1890x^512+1512x^513+1386x^514+11508x^515+9618x^516+1218x^517+1488x^518+2604x^519+1596x^520+1428x^521+9660x^522+6678x^523+966x^524+18x^525+24x^532+12x^539

The gray image is a linear code over GF(7) with n=595, k=6 and d=494.
This code was found by Heurico 1.16 in 6.24 seconds.