The generator matrix
1 0 1 1 1 0 X 1 1
0 1 X+1 X^2+X X^2+1 1 0 0 0
0 0 X^3 0 0 0 X^3 0 0
0 0 0 X^3 0 0 X^3 0 0
0 0 0 0 X^3 0 X^3 0 0
0 0 0 0 0 X^3 X^3 0 0
generates a code of length 9 over Z2[X]/(X^4) who´s minimum homogenous weight is 4.
Homogenous weight enumerator: w(x)=1x^0+23x^4+96x^5+32x^6+224x^7+717x^8+1920x^9+696x^10+224x^11+53x^12+96x^13+8x^14+6x^16
The gray image is a linear code over GF(2) with n=72, k=12 and d=16.
This code was found by Heurico 1.16 in 0.015 seconds.