The generator matrix

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

generates a code of length 31 over Z7[X]/(X^2) who´s minimum homogenous weight is 168.

Homogenous weight enumerator: w(x)=1x^0+444x^168+840x^169+420x^170+1992x^175+6300x^176+1680x^177+9456x^182+26040x^183+5670x^184+18552x^189+38850x^190+6636x^191+348x^196+228x^203+150x^210+42x^217

The gray image is a linear code over GF(7) with n=217, k=6 and d=168.
This code was found by Heurico 1.16 in 3.28 seconds.