The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+26x^4+160x^5+869x^6+1984x^7+869x^8+160x^9+26x^10+1x^14

The gray image is a linear code over GF(2) with n=56, k=12 and d=16.
This code was found by Heurico 1.16 in 0.016 seconds.