The generator matrix

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

generates a code of length 7 over Z2[X]/(X^4) who´s minimum homogenous weight is 5.

Homogenous weight enumerator: w(x)=1x^0+26x^5+130x^6+206x^7+119x^8+22x^9+6x^10+2x^11

The gray image is a linear code over GF(2) with n=56, k=9 and d=20.
This code was found by Heurico 1.16 in 3.62e-008 seconds.