The generator matrix

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

generates a code of length 27 over Z7[X]/(X^2) who´s minimum homogenous weight is 147.

Homogenous weight enumerator: w(x)=1x^0+1254x^147+2754x^154+6198x^161+5868x^168+378x^175+354x^182

The gray image is a linear code over GF(7) with n=189, k=5 and d=147.
This code was found by Heurico 1.16 in 13 seconds.