The generator matrix

 1  1  1  1  1  1  1  1  X  X  X
 0 X^3+X^2  0 X^3+X^2  0  0 X^3  0 X^3+X^2 X^3+X^2 X^3
 0  0 X^3  0  0  0 X^3  0 X^3 X^3  0
 0  0  0 X^3  0  0  0 X^3 X^3  0 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 X^3 X^3 X^3 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+66x^8+32x^9+48x^10+704x^11+104x^12+32x^13+16x^14+21x^16

The gray image is a linear code over GF(2) with n=88, k=10 and d=32.
This code was found by Heurico 1.16 in 0.078 seconds.