The generator matrix

 1  1  1  1  0  0 X^3
 0  X  0  X  X  X  X
 0  0  X  X X^3+X^2  0 X^2
 0  0  0 X^3  0 X^3 X^3
 0  0  0  0 X^3 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+122x^4+160x^5+773x^6+1984x^7+773x^8+160x^9+122x^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 seconds.