The generator matrix

 1  1  1  1  X X^3  1  1  X X^2  1
 0  X  0 X^3+X^2+X X^2+X  X X^2  X X^3 X^2 X^3+X
 0  0 X^3+X^2 X^2 X^3 X^2 X^2 X^3+X^2 X^3+X^2 X^3+X^2 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+60x^9+142x^10+144x^11+94x^12+44x^13+18x^14+8x^15+1x^16

The gray image is a linear code over GF(2) with n=88, k=9 and d=36.
This code was found by Heurico 1.16 in 0 seconds.