The generator matrix

 1  1  1  1 X^3 X^3+X^2  1  1  1
 0  X  0  X  X  X X^3+X  X X^2+X
 0  0  X  X X^2 X^2+X X^2+X X^2 X^2+X
 0  0  0 X^3  0  0 X^3 X^3  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+35x^6+144x^7+413x^8+872x^9+410x^10+128x^11+34x^12+8x^13+3x^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 0.015 seconds.