The generator matrix

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

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+26x^4+128x^5+352x^6+1032x^7+365x^8+112x^9+24x^10+8x^11

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 3.81e-009 seconds.