The generator matrix

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

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+98x^8+64x^9+528x^10+640x^11+584x^12+64x^13+48x^14+21x^16

The gray image is a linear code over GF(2) with n=88, k=11 and d=32.
This code was found by Heurico 1.16 in 0.766 seconds.