The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+346x^4+1184x^5+6437x^6+16832x^7+6437x^8+1184x^9+346x^10+1x^14

The gray image is a linear code over GF(2) with n=56, k=15 and d=16.
This code was found by Heurico 1.16 in 10.8 seconds.