The generator matrix

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

generates a code of length 18 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+654x^16+768x^18+608x^20+16x^24+1x^32

The gray image is a code over GF(2) with n=144, k=11 and d=64.
This code was found by Heurico 1.16 in 5.36 seconds.