The generator matrix

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

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+1176x^36+2520x^42+14112x^43+43218x^48+14160x^49+42336x^50+126x^56

The gray image is a linear code over GF(7) with n=56, k=6 and d=36.
This code was found by Heurico 1.16 in 0.196 seconds.