The generator matrix

 1  0  1  1  1 X^2+X  1  1  X  X  1
 0  1 X+1 X^2+X X^3+X^2+1  1 X^3 X^3+X^2+X X^3+X^2+X  X  0
 0  0 X^2  0 X^3+X^2 X^3 X^2 X^3+X^2 X^2 X^3+X^2  0
 0  0  0 X^3 X^3 X^3  0  0  0 X^3  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+69x^8+164x^9+509x^10+572x^11+502x^12+156x^13+66x^14+4x^15+4x^16+1x^18

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 0.015 seconds.