The generator matrix

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

generates a code of length 31 over Z7[X]/(X^2) who´s minimum homogenous weight is 182.

Homogenous weight enumerator: w(x)=1x^0+258x^182+840x^183+210x^184+366x^189+630x^190+84x^191+12x^196

The gray image is a linear code over GF(7) with n=217, k=4 and d=182.
This code was found by Heurico 1.16 in 0.00354 seconds.