The generator matrix

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

generates a code of length 7 over Z7[X]/(X^2) who´s minimum homogenous weight is 21.

Homogenous weight enumerator: w(x)=1x^0+210x^21+840x^28+3402x^35+107478x^42+5718x^49

The gray image is a linear code over GF(7) with n=49, k=6 and d=21.
This code was found by Heurico 1.16 in 0.282 seconds.