The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+58x^18+2x^20+2x^22+1x^24

The gray image is a code over GF(2) with n=144, k=6 and d=72.
This code was found by Heurico 1.16 in 0.016 seconds.