The generator matrix

 1  1  1  1  1  1  1  1  X  X  1
 0 X^3+X^2  0  0 X^3 X^3+X^2 X^3+X^2 X^2 X^2 X^2  0
 0  0 X^3+X^2  0 X^3+X^2 X^3+X^2 X^2 X^3 X^2 X^3+X^2  0
 0  0  0 X^3+X^2 X^2 X^3 X^2 X^2  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+45x^8+98x^9+19x^10+704x^11+18x^12+92x^13+42x^14+2x^17+3x^18

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 -1.01e-007 seconds.