The generator matrix

 1  0  1  1  1 X^2+X  1  1  1  1  0
 0  1 X+1 X^2+X X^3+X^2+1  1 X^3 X^3+X^2+X X^3+X^2 X+1  1
 0  0 X^2  0 X^3+X^2 X^3 X^2 X^3+X^2  0  0 X^3
 0  0  0 X^3  0 X^3  0 X^3 X^3  0  0
 0  0  0  0 X^3  0 X^3  0 X^3 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+72x^8+288x^9+888x^10+1600x^11+892x^12+288x^13+56x^14+11x^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 0.031 seconds.