The generator matrix

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

generates a code of length 9 over Z4[X]/(X^2+2X+2) 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 6.31 seconds.