The generator matrix

 1  1  1  1  1  1  1  1 X^2  1  1
 0 X^3+X^2  0 X^3+X^2  0 X^3 X^3+X^2 X^2 X^3  0  0
 0  0 X^3  0  0 X^3 X^3 X^3  0  0  0
 0  0  0 X^3 X^3 X^3 X^3  0  0  0  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+13x^8+56x^10+128x^11+43x^12+8x^14+6x^16+1x^20

The gray image is a linear code over GF(2) with n=88, k=8 and d=32.
This code was found by Heurico 1.16 in 3.81e-009 seconds.