The generator matrix

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

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+14x^5+34x^6+166x^7+23x^8+10x^9+6x^10+2x^11

The gray image is a linear code over GF(2) with n=56, k=8 and d=20.
This code was found by Heurico 1.16 in 6.87e-008 seconds.