The generator matrix

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

generates a code of length 11 over Z2[X]/(X^4) who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+21x^8+48x^9+9x^10+352x^11+10x^12+48x^13+22x^14+1x^18

The gray image is a linear code over GF(2) with n=88, k=9 and d=32.
This code was found by Heurico 1.16 in 0 seconds.