The generator matrix

 1  1  1  1  X X^2  1  1  X  1  1
 0 X^3+X^2  0 X^3+X^2 X^3+X^2 X^2  0 X^3+X^2 X^3+X^2  0  0
 0  0 X^3  0  0  0  0 X^3  0  0 X^3
 0  0  0 X^3  0  0  0 X^3  0 X^3 X^3
 0  0  0  0 X^3  0  0  0 X^3 X^3  0
 0  0  0  0  0 X^3  0 X^3 X^3  0  0
 0  0  0  0  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 6.

Homogenous weight enumerator: w(x)=1x^0+17x^6+77x^8+64x^9+545x^10+640x^11+547x^12+64x^13+75x^14+14x^16+3x^18+1x^20

The gray image is a linear code over GF(2) with n=88, k=11 and d=24.
This code was found by Heurico 1.16 in 0.016 seconds.