The generator matrix

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

generates a code of length 20 over Z7[X]/(X^2) who´s minimum homogenous weight is 112.

Homogenous weight enumerator: w(x)=1x^0+120x^112+126x^119+2058x^120+42x^126+18x^133+36x^140

The gray image is a linear code over GF(7) with n=140, k=4 and d=112.
This code was found by Heurico 1.16 in 0.00246 seconds.