The generator matrix

 1  0  1  1  1 X^3+X^2  1  1  X  1  1
 0  1  1 X^2 X^3+X+1  1  X  0 X^3+X X^2  0
 0  0  X  X X^2 X^2+X X^3+X X^3+X^2+X X^2+X X^2 X^3
 0  0  0 X^3  0  0 X^3 X^3  0 X^3  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+92x^8+336x^9+744x^10+1760x^11+740x^12+336x^13+72x^14+15x^16

The gray image is a linear code over GF(2) with n=88, k=12 and d=32.
This code was found by Heurico 1.16 in 0.015 seconds.