The generator matrix

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

generates a code of length 11 over Z7[X]/(X^2) who´s minimum homogenous weight is 49.

Homogenous weight enumerator: w(x)=1x^0+144x^49+882x^54+414x^56+10290x^60+10584x^61+534x^63+61740x^67+31752x^68+876x^70+432x^77

The gray image is a linear code over GF(7) with n=77, k=6 and d=49.
This code was found by Heurico 1.16 in 0.533 seconds.