The generator matrix
1 0 0 0 1 1 1 1 1
0 1 0 0 X X^2+1 1 X+1 X^2
0 0 1 0 X+1 1 X X^3+1 0
0 0 0 1 1 X X+1 X^3+1 X
generates a code of length 9 over Z2[X]/(X^4) who´s minimum homogenous weight is 5.
Homogenous weight enumerator: w(x)=1x^0+72x^5+636x^6+3864x^7+14454x^8+27464x^9+14496x^10+3848x^11+616x^12+80x^13+4x^14+1x^16
The gray image is a linear code over GF(2) with n=72, k=16 and d=20.
This code was found by Heurico 1.16 in 2.19 seconds.