The generator matrix

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

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+58x^6+104x^7+521x^8+688x^9+508x^10+104x^11+62x^12+2x^14

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 0.016 seconds.