The generator matrix

 1  1  1  1  0  1  X  1  1
 0  X  0  X  X X^3+X^2  0  0 X^3
 0  0  X  X X^3+X^2  0 X^2+X  0 X^2
 0  0  0 X^3  0 X^3  0 X^3  0
 0  0  0  0 X^3 X^3 X^3  0  0

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+18x^5+68x^6+282x^7+702x^8+1956x^9+696x^10+292x^11+64x^12+10x^13+4x^14+2x^15+1x^16

The gray image is a linear code over GF(2) with n=72, k=12 and d=20.
This code was found by Heurico 1.16 in 0.015 seconds.