The generator matrix

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

generates a code of length 27 over Z7[X]/(X^2) who´s minimum homogenous weight is 140.

Homogenous weight enumerator: w(x)=1x^0+66x^140+84x^144+168x^145+420x^146+1188x^147+882x^150+1512x^151+1260x^152+1680x^153+2652x^154+10584x^157+9072x^158+5208x^159+5670x^160+6210x^161+31752x^164+18144x^165+7770x^166+6636x^167+6060x^168+354x^175+222x^182+54x^189

The gray image is a linear code over GF(7) with n=189, k=6 and d=140.
This code was found by Heurico 1.16 in 2.01 seconds.