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

generates a code of length 27 over Z7[X]/(X^2) who´s minimum homogenous weight is 133.

Homogenous weight enumerator: w(x)=1x^0+366x^133+1308x^140+1590x^147+2694x^154+2922x^161+100842x^162+3696x^168+2916x^175+1098x^182+216x^189

The gray image is a linear code over GF(7) with n=189, k=6 and d=133.
This code was found by Heurico 1.16 in 4.98 seconds.