The generator matrix

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

generates a code of length 28 over Z7[X]/(X^2) who´s minimum homogenous weight is 159.

Homogenous weight enumerator: w(x)=1x^0+2100x^159+150x^161+882x^162+3150x^166+108x^168+5292x^169+5040x^173+36x^175+12x^182+30x^189+6x^196

The gray image is a linear code over GF(7) with n=196, k=5 and d=159.
This code was found by Heurico 1.16 in 66 seconds.