The generator matrix

 1  0  1  1  1 X^3+X  1  0  1  X  1
 0  1  1 X^3+X^2 X^3+X+1  1  X  0 X^3+X  0 X^3
 0  0  X X^2+X X^2 X^2+X X^3+X  X X^3+X^2+X X^2 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+29x^8+216x^9+368x^10+832x^11+390x^12+152x^13+40x^14+16x^15+4x^16

The gray image is a linear code over GF(2) with n=88, k=11 and d=32.
This code was found by Heurico 1.16 in 0.031 seconds.