The generator matrix

 1  0  0  1  1  1  1
 0  1  0  X X^2+1 X^2+X  0
 0  0  1  1 X+1 X^2+1  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+59x^4+280x^5+597x^6+2226x^7+594x^8+276x^9+59x^10+2x^11+2x^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 0.046 seconds.