The generator matrix

 1  1  1  1  1  1  1  1 X^2 X^3  1
 0  X X^3+X^2 X^2+X  0 X^2+X  0 X^2+X X^3+X^2 X^3  0
 0  0 X^3  0  0 X^3 X^3 X^3  0 X^3  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+17x^8+88x^9+77x^10+152x^11+86x^12+72x^13+2x^14+8x^15+8x^16+1x^18

The gray image is a linear code over GF(2) with n=88, k=9 and d=32.
This code was found by Heurico 1.16 in -3.24e-008 seconds.