The generator matrix

 1  0  0  0  1  1  1
 0  1  0  0  X X^2+1  0
 0  0  1  0 X+1  1  0
 0  0  0  1  1  X  0
 0  0  0  0 X^3  0 X^3

generates a code of length 7 over Z2[X]/(X^4) who´s minimum homogenous weight is 3.

Homogenous weight enumerator: w(x)=1x^0+130x^3+1002x^4+5528x^5+24085x^6+69580x^7+24085x^8+5528x^9+1002x^10+130x^11+1x^14

The gray image is a linear code over GF(2) with n=56, k=17 and d=12.
This code was found by Heurico 1.16 in 3.87 seconds.