The generator matrix

 1  1  1  1  X  1  1  1  1
 0  X  0 X^2+X+2 X^2+X  2 X^2 X^2+X  0
 0  0 X^2+2  0  0  2 X^2+2 X^2+2  0
 0  0  0 X^2+2  0 X^2+2  2 X^2  2
 0  0  0  0  2  0  2  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+30x^5+70x^6+170x^7+694x^8+2156x^9+708x^10+180x^11+56x^12+22x^13+6x^14+2x^15+1x^16

The gray image is a code over GF(2) with n=72, k=12 and d=20.
This code was found by Heurico 1.16 in 0.016 seconds.