The generator matrix
1 1 1 1 X 1 1 X^2 X^3+X^2
0 X 0 X X^2 X^2+X X^3 X X^2
0 0 X X X X^2+X 0 X^2+X X
0 0 0 X^2 0 X^3 X^3+X^2 X^2 X^2
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+106x^6+256x^7+989x^8+1408x^9+968x^10+256x^11+106x^12+6x^14
The gray image is a linear code over GF(2) with n=72, k=12 and d=24.
This code was found by Heurico 1.16 in 0.328 seconds.