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

generates a code of length 96 over Z7[X]/(X^2) who´s minimum homogenous weight is 560.

Homogenous weight enumerator: w(x)=1x^0+1554x^560+4536x^561+4494x^562+4284x^563+4062x^567+8316x^568+8778x^569+7140x^570+4890x^574+8610x^575+9744x^576+6678x^577+4098x^581+8484x^582+6174x^583+5418x^584+4254x^588+7098x^589+5796x^590+3234x^591+6x^616

The gray image is a linear code over GF(7) with n=672, k=6 and d=560.
This code was found by Heurico 1.16 in 11.5 seconds.