The generator matrix

 1  0  1  1  1  0  X
 0  1 X+1 X^2+X X^2+1  1  0
 0  0 X^3  0  0  0 X^3
 0  0  0 X^3  0  0 X^3
 0  0  0  0 X^3  0 X^3
 0  0  0  0  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+45x^4+224x^5+712x^6+2112x^7+747x^8+224x^9+24x^10+7x^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 0.015 seconds.