The generator matrix

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

generates a code of length 10 over Z7[X]/(X^2) who´s minimum homogenous weight is 55.

Homogenous weight enumerator: w(x)=1x^0+420x^55+30x^56+882x^60+1050x^62+18x^70

The gray image is a linear code over GF(7) with n=70, k=4 and d=55.
This code was found by Heurico 1.16 in 0.000429 seconds.