The generator matrix

 1  0  1  1  1 X^2+X  1
 0  1 X+1 X^2+X X^2+1  1  0
 0  0 X^3 X^3  0 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+16x^5+126x^6+224x^7+127x^8+16x^9+2x^10

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 1.05e-007 seconds.