The generator matrix

 1  1  1  X  1  X  1
 0 X^3  0 X^3 X^3  0  0

generates a code of length 7 over Z2[X]/(X^4) who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+1x^6+26x^7+1x^8+2x^9+1x^10

The gray image is a linear code over GF(2) with n=56, k=5 and d=24.
This code was found by Heurico 1.16 in 3.81e-009 seconds.