The generator matrix

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

generates a code of length 28 over Z7[X]/(X^2) who´s minimum homogenous weight is 140.

Homogenous weight enumerator: w(x)=1x^0+594x^140+1248x^147+1908x^154+2658x^161+103872x^168+3444x^175+2724x^182+1074x^189+126x^196

The gray image is a linear code over GF(7) with n=196, k=6 and d=140.
This code was found by Heurico 1.16 in 5.22 seconds.