The generator matrix

 1  0  0  1  1  1 X^2
 0  1  0  1 X^2+X X^3+X^2  1
 0  0  1  1 X+1  1  X
 0  0  0 X^3+X^2  0 X^2 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+92x^4+736x^5+3352x^6+8008x^7+3385x^8+720x^9+80x^10+8x^11+2x^12

The gray image is a linear code over GF(2) with n=56, k=14 and d=16.
This code was found by Heurico 1.16 in 0.125 seconds.