The generator matrix

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

generates a code of length 21 over Z7[X]/(X^2) who´s minimum homogenous weight is 105.

Homogenous weight enumerator: w(x)=1x^0+78x^105+444x^112+456x^119+2058x^120+408x^126+12348x^127+510x^133+426x^140+78x^147

The gray image is a linear code over GF(7) with n=147, k=5 and d=105.
This code was found by Heurico 1.16 in 0.0786 seconds.