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.