The generator matrix

 1  1  X  1  1  1  1
 0 X^3+X^2 X^3+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  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+8x^4+40x^6+160x^7+37x^8+8x^10+2x^12

The gray image is a linear code over GF(2) with n=56, k=8 and d=16.
This code was found by Heurico 1.16 in 6.87e-008 seconds.