The generator matrix

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

generates a code of length 9 over Z2[X]/(X^4) who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+46x^6+80x^7+593x^8+608x^9+593x^10+80x^11+46x^12+1x^18

The gray image is a linear code over GF(2) with n=72, k=11 and d=24.
This code was found by Heurico 1.16 in 0 seconds.