The generator matrix

 1  0  0  0  1  1  1  1
 0  1  0  0  X X^2+1 X^3+X^2+X X^2
 0  0  1  0 X+1  1 X^3+X^2+1 X^2
 0  0  0  1  1  X X^2+X  0

generates a code of length 8 over Z2[X]/(X^4) who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+58x^4+548x^5+3149x^6+14272x^7+29437x^8+14360x^9+3122x^10+512x^11+72x^12+4x^13+1x^14

The gray image is a linear code over GF(2) with n=64, k=16 and d=16.
This code was found by Heurico 1.16 in 1.2 seconds.