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

generates a code of length 94 over Z7[X]/(X^2) who´s minimum homogenous weight is 539.

Homogenous weight enumerator: w(x)=1x^0+174x^539+168x^540+84x^541+2520x^545+1056x^546+1722x^547+1302x^548+8484x^552+2634x^553+4536x^554+2352x^555+11466x^559+3486x^560+6720x^561+3696x^562+18270x^566+5676x^567+10500x^568+4620x^569+14238x^573+3270x^574+5166x^575+2352x^576+2646x^580+114x^581+126x^588+84x^595+30x^602+66x^609+24x^616+42x^623+12x^630+6x^637+6x^644

The gray image is a linear code over GF(7) with n=658, k=6 and d=539.
This code was found by Heurico 1.16 in 8.5 seconds.