The generator matrix

 1  1  1  1  1  X  1  1  1  1  1
 0 X^3+X^2  0 X^2  0 X^3 X^2  0 X^3+X^2 X^3 X^3+X^2
 0  0 X^3+X^2 X^2 X^3 X^2 X^3+X^2 X^2 X^3 X^3 X^3+X^2

generates a code of length 11 over Z2[X]/(X^4) who´s minimum homogenous weight is 9.

Homogenous weight enumerator: w(x)=1x^0+10x^9+31x^10+176x^11+30x^12+2x^13+1x^14+4x^15+1x^20

The gray image is a linear code over GF(2) with n=88, k=8 and d=36.
This code was found by Heurico 1.16 in 3.81e-009 seconds.