The generator matrix
1 0 0 0 1 1 1 1 1
0 1 0 0 X^2 1 X^2+X+1 X^2+X+1 X+1
0 0 1 0 X^2+1 X+1 X 0 X+1
0 0 0 1 1 X X+1 X 0
0 0 0 0 2 0 0 2 2
generates a code of length 9 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 5.
Homogenous weight enumerator: w(x)=1x^0+144x^5+1336x^6+7552x^7+29118x^8+54752x^9+29152x^10+7552x^11+1312x^12+144x^13+8x^14+1x^16
The gray image is a code over GF(2) with n=72, k=17 and d=20.
This code was found by Heurico 1.16 in 6.06 seconds.