The generator matrix

 1  0  0  1  1  1 X^2+X  1  1
 0  1  0  1 X^2+2 X^2+3  1  X  0
 0  0  1  1  0 X+1  X  3  0
 0  0  0  X X^2+X X^2 X+2  0  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+96x^5+434x^6+1554x^7+6710x^8+15144x^9+6780x^10+1532x^11+408x^12+104x^13+2x^14+2x^15+1x^16

The gray image is a code over GF(2) with n=72, k=15 and d=20.
This code was found by Heurico 1.16 in 0.484 seconds.