The generator matrix

 1  1  1  1  1  1  1
 0 X^3+X^2  0  0 X^3 X^3+X^2  0
 0  0 X^3+X^2  0 X^3+X^2 X^3+X^2 X^3
 0  0  0 X^3+X^2 X^2 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+26x^4+32x^5+37x^6+832x^7+37x^8+32x^9+26x^10+1x^14

The gray image is a linear code over GF(2) with n=56, k=10 and d=16.
This code was found by Heurico 1.16 in 6.87e-008 seconds.