The generator matrix

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

generates a code of length 8 over Z7[X]/(X^2) who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+126x^36+756x^42+1512x^43+6174x^48+3576x^49+4536x^50+126x^56

The gray image is a linear code over GF(7) with n=56, k=5 and d=36.
This code was found by Heurico 1.16 in 0.0049 seconds.