The generator matrix

 1  1  1  1  X  0  1  1  1  1  X
 0  X X^3+X^2 X^2+X X^2+X  X  0  0 X^3+X^2 X^3+X^2 X^3+X^2
 0  0 X^3  0  0 X^3  0 X^3  0 X^3  0
 0  0  0 X^3  0 X^3 X^3 X^3  0  0  0
 0  0  0  0 X^3 X^3  0  0 X^3 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+44x^8+32x^9+272x^10+320x^11+284x^12+32x^13+32x^14+7x^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 3.81e-009 seconds.