The generator matrix

 1  0  1  1  1 X^3  1
 0  1 X+1 X^3+X^2+X X^2+1  1 X^3
 0  0 X^2 X^3+X^2 X^3 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+42x^5+226x^6+494x^7+215x^8+38x^9+6x^10+2x^11

The gray image is a linear code over GF(2) with n=56, k=10 and d=20.
This code was found by Heurico 1.16 in 0.047 seconds.