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.