The generator matrix

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

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+75x^4+64x^5+816x^6+2176x^7+831x^8+64x^9+64x^10+5x^12

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.