The generator matrix

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

generates a code of length 11 over Z2[X]/(X^4) who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+79x^6+656x^7+2904x^8+9954x^9+27974x^10+47896x^11+28041x^12+9964x^13+2859x^14+648x^15+93x^16+2x^17+1x^20

The gray image is a linear code over GF(2) with n=88, k=17 and d=24.
This code was found by Heurico 1.16 in 8.16 seconds.