The generator matrix

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

generates a code of length 17 over Z7[X]/(X^2) who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+168x^84+498x^91+450x^98+14406x^102+510x^105+612x^112+162x^119

The gray image is a linear code over GF(7) with n=119, k=5 and d=84.
This code was found by Heurico 1.16 in 0.0574 seconds.