The generator matrix

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

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+126x^9+186x^10+398x^11+160x^12+106x^13+22x^14+10x^15+2x^16

The gray image is a linear code over GF(2) with n=88, k=10 and d=32.
This code was found by Heurico 1.16 in 3.62e-008 seconds.