The generator matrix

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

generates a code of length 17 over Z7[X]/(X^2) who´s minimum homogenous weight is 77.

Homogenous weight enumerator: w(x)=1x^0+432x^77+1230x^84+2070x^91+14406x^96+3420x^98+86436x^103+5052x^105+3414x^112+1188x^119

The gray image is a linear code over GF(7) with n=119, k=6 and d=77.
This code was found by Heurico 1.16 in 2.45 seconds.