The generator matrix
1 1 1 1 X X X^2 X^2 1
0 X^3 0 X^3 X^3 0 X^3 0 0
generates a code of length 9 over Z2[X]/(X^4) who´s minimum homogenous weight is 8.
Homogenous weight enumerator: w(x)=1x^0+1x^8+24x^9+2x^10+4x^11
The gray image is a linear code over GF(2) with n=72, k=5 and d=32.
This code was found by Heurico 1.16 in -1.01e-007 seconds.