The generator matrix

 1  1  1  1  1  X  1 X^2  1
 0  X  0 X^2+X X^2 X^2+X X^3+X^2+X X^3  0
 0  0 X^3+X^2  0 X^2 X^3 X^2 X^2  0
 0  0  0 X^3 X^3 X^3 X^3 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+17x^6+84x^7+239x^8+352x^9+236x^10+68x^11+16x^12+8x^13+3x^14

The gray image is a linear code over GF(2) with n=72, k=10 and d=24.
This code was found by Heurico 1.16 in -1.01e-007 seconds.