The generator matrix

 1  0  1  1  1 X^3+X^2+X  1
 0  1  1 X^3+X^2 X^3+X+1  1  0
 0  0  X X^2+X X^2 X^2  0
 0  0  0 X^3  0 X^3 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+38x^4+142x^5+824x^6+2090x^7+825x^8+130x^9+40x^10+6x^11

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.