The generator matrix

 1  1  1  1  0  1  1 X^3  X  1  1
 0  X  0  X  X X^3 X^2 X^2 X^3+X X^3 X^3
 0  0  X  X X^3+X^2 X^2  X  X X^2+X X^3 X^3+X^2+X
 0  0  0 X^3  0 X^3  0 X^3 X^3  0  0
 0  0  0  0 X^3 X^3 X^3 X^3 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+194x^8+192x^9+944x^10+1408x^11+1000x^12+192x^13+144x^14+21x^16

The gray image is a linear code over GF(2) with n=88, k=12 and d=32.
This code was found by Heurico 1.16 in 20.3 seconds.