The generator matrix

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

generates a code of length 13 over Z7[X]/(X^2) who´s minimum homogenous weight is 63.

Homogenous weight enumerator: w(x)=1x^0+318x^63+444x^70+504x^77+14406x^78+834x^84+300x^91

The gray image is a linear code over GF(7) with n=91, k=5 and d=63.
This code was found by Heurico 1.16 in 0.0391 seconds.