The generator matrix

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

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+51x^4+76x^5+334x^6+1128x^7+329x^8+76x^9+50x^10+3x^12

The gray image is a linear code over GF(2) with n=56, k=11 and d=16.
This code was found by Heurico 1.16 in 0.016 seconds.