The generator matrix

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

generates a code of length 11 over Z2[X]/(X^4) who´s minimum homogenous weight is 9.

Homogenous weight enumerator: w(x)=1x^0+22x^9+174x^10+116x^11+175x^12+22x^13+1x^14+1x^18

The gray image is a linear code over GF(2) with n=88, k=9 and d=36.
This code was found by Heurico 1.16 in 6.87e-008 seconds.