The generator matrix

 1  0  1  1  1  1 X^2+X  1  1  1  X
 0  1 X+1 X^2+X X^3+X^2+X+1 X^2+1  1 X^3+1 X+1 X^2+1  0
 0  0 X^3  0  0  0  0 X^3  0 X^3 X^3
 0  0  0 X^3  0  0 X^3 X^3  0 X^3  0
 0  0  0  0 X^3  0  0 X^3 X^3  0 X^3
 0  0  0  0  0 X^3  0 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+98x^8+256x^9+1040x^10+1280x^11+1096x^12+256x^13+48x^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 15.6 seconds.