The generator matrix

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

generates a code of length 7 over Z2[X]/(X^3) who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+10x^6+8x^7+11x^8+2x^10

The gray image is a linear code over GF(2) with n=28, k=5 and d=12.
This code was found by Heurico 1.16 in 9.8e-005 seconds.